Shawn Found That a Solution of X 3
Tutors Answer Your Questions about Linear Equations And Systems Word Problems (FREE)
Question 1188364: A truck rental company charges Php3000 to rent a truck for
the day, plus an additional charge of Php50 per liter of
gasoline consumed.
Answer by ikleyn(42255)
Question 1188312: A boat costs $11,000. What is the length of the boat?
Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(67885)
Answer by math_helper(2282)
Question 1188253: help me solve this linear equation word problem:
A salesperson receives a base salary of $35,000 and a commission of
10% of the total sales for the year.
a. Write a linear model that shows the salesperson's total income
based on total sales of k dollars.
b. If the salesperson sells $250,000 worth of merchandise, what is
her total income for the year, including her base salary?
Answer by MathLover1(19126)
You can put this solution on YOUR website! b.
Total Income is % sales plus
a.
= total Income
= sales
To find total income replace with
and solve for
Question 1188214: John filled the gas tank of his car with 32.4 litres of gas just before starting on a trip. He noticed that the odometer read 30,803 km when he left the gas station. When he stopped for lunch, he saw the next palindrome on his odometer. He then filled up with 42 litres of gas at the palindrome after the one he saw at lunch. What was the average number of litres per 100 km used by his car during the trip?
Answer by Alan3354(67885)
Question 1188233: Two consecutive odd number are chosen so that one third of the smaller exceed one seventh of the larger by 6.find the numbers.
Answer by math_helper(2282)
You can put this solution on YOUR website!
(1/3)n = (1/7)(n+2) + 6
n = 33, n+2 = 35
Check:
(1/3)n = (1/3)(33) = 11
and
(1/7)(n+2)+6 = (1/7)(35)+6 = 5+6 = 11 (ok)
Question 1188210: A cylinder has a radius of x + 2 units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function. The formula for the volume of a cylinder is V=Ï€r2h
Question 7 options:
3x2π + 12xπ + 12π
(xπ + 2π2) 3
(3Ï€)(x+2)2
Answer by Alan3354(67885)
You can put this solution on YOUR website!
A cylinder has a radius of x + 2 units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function. The formula for the volume of a cylinder is V=Ï€r2h
---------------
r = x+2
h = x+5
Question 1188211: You are designing boxes to ship your newest design. You use a rectangular piece of cardboard measuring 40 in. by 30 in. to be make an open box with a base (bottom) of 900 in2 by cutting equal squares from the four corners and then bending up the sides. Find, to the nearest tenth of an inch, the length of the side of the square that must be cut from each corner.
Question 3 options:
4 in
37.5 in
2.5 inches
Answer by Boreal(14500)
You can put this solution on YOUR website!
Can exclude 37.5 in right away given that it is impossible.
the bottom will be 40-2x by 30-2x, and that will equal 900 in^2. x is the length of the side of the square.
1200-140x+4x^2=900
4x^2-140x+300=0
x^2-35x+75=0
x=(1/2)(35+/- sqrt (1225-300)); sqrt 925=30.4
x=32.7 inches and 2.3 inches; 2.3 inches is the answer.
the sides will become 35.4 x 25.4=899.16 in^2.
The best choice is 2.5 inches
Question 1187751: Please help me solve this (it is based on matrices as there was no option to select that I chose word problems only):
Statistics show that at a certain university, 70% of the students who live on campus during a given semester will remain on campus the following semester, and 90% of students living off campus during a given semester will remain off campus the following semester. Let x and y denote the number of students who live on and off campus this semester, and let u and v be the corresponding numbers for the next semester. Then,
0 . 7 x + 0 . 1 y = u
0.3x + 0.9y = v
(a) Write this system of equations in matrix form.
(b) Solve the resulting matrix equation for [x
y]
(c) Suppose that, out of a group of 9000 students, 6000 currently live on campus and 3000 live off campus. How many lived on campus last semester? How many will live off campus next semester?
Answer by Theo(11797)
You can put this solution on YOUR website! 6000 currently live on campus and 3000 currently live off campus. since x is the number who live on campus this semester and y is the number who currrently live off campus this summer, then you get: x = 6000 and y = 3000. your first equation is the ones who will be living on campus next semester. of the 6000 that are currently living on campus, 70% will still live on campus next semester. your second equation is the ones who will be living off campus next semeste. of the 6000 that are currently living on campus, 30% will live off campus next semester. for part a i get the following: the matrix is: normally, u and v would be constants. for part b, i get the following: that completes part b. from part c, we know that both u and v = 4500 each. to confirm part b was done correctly, replace u and v with 4500 to get: i believe this satisfies the requirements for this problem. solving part c first helped me in analyzing parts a and b because i had some number to check my answers for part a and b against. here's a reference on matrix operations you might find helpful. https://www.studypug.com/algebra-help/the-three-types-of-matrix-row-operations?camp_id=1026250253&grp_id=112411027342&kw=&mt=&source=g&pos=&tgt=dsa-19959388920&loc=9003567&device=c&adid=529422243034&gclid=EAIaIQobChMItIvzlf-59AIVg2pvBB3u6wjTEAMYAiAAEgLzxPD_BwE theo
for part c, i get the following:
of the 3000 that are currently living off campus, 10% will be living on campus next semester.
.7x + .1y = u becomes .7*6000 + .1*3000 = 4500 that will be living on campus next semeste.
of the 3000 that are currently living off campus, 90% will continue to live off campus next semester.
.3x + .9y = v becomes .3*6000 + .9*3000 = 4500 that will be living off campus next semester. tableau 1 row 1 equals .7 .1 u tableau 1 row 2 equals .3 .9 v
since i didn't know their value up front (i learaned it in part c), i left them as u and v. start with: tableau 1 row 1 equals .7 .1 u tableau 1 row 2 equals .3 .9 v tableau 2 row 1 equals 9 * tableau 1 row 1 minus tableau 1 row 2. tableau 2 row 2 equals tableau 1 row 2. you get: tableau 2 row 1 equals 6 0 9u - v tableau 2 row 2 equals .3 .9 v tableau 3 row 1 equals tableau 2 row 1 tableau 3 row 2 = tableau 2 row 2 minus .05 * tableau 2 row 1. you get: tableau 3 row 1 equals 6 0 9u - v tableau 3 row 2 equals 0 .9 v - .45u + .05v tableau 4 row 1 equals tableau 3 row 1 divided by 6. tableau 4 row 2 equals tableau 3 row 2 divided by .9. you get: tableau 4 row 1 equals 1 0 (9u - v) / 6 tableau 4 row 2 equals 0 1 (1.05v - .45u) / .9
tableau 4 row 1 equals 1 0 (9*4500-4500)/6 = 6000 tableau 4 row 2 equals 0 1 (1.05*4500 - .45*4500) / .9 = 3000
since we already know that x was equal to 6000 and y was equal to 3000 because that was given to us, this confirms the matrix equation was modeled correctly.
let me know if you have any questions.
Question 1187750: Milan the trainer has two solo workout plans that he offers his clients: Plan A and Plan B.
Each client does either one or the other (not both).
On Friday there were 3 clients who did Plan A and 2 who did Plan B.
On Saturday there were 8 clients who did Plan A and 4 who did Plan B.
Milan trained his Friday clients for a total of 7hours and his Saturday clients for a total of 17hours.
How long does each of the workout plans last?
Answer by Theo(11797)
You can put this solution on YOUR website! on friday, there were 3 who did plan A and 2 who did plan B for a total of 7 hours. on saturday, there were 8 who did plan A and 4 who did plan B for a total of 17 hours. you have two equations that need to be solved simultaneously. the requations are: 3a + 2b = 7 multiply both sides of the first equAtion by 2 and leave the second equation as is to get: 6a + 4b = 14 subtract the first equation from the second to get: 2a = 3 solve for a to get: a = 3/2 replace a with 3/2 in either equation to get: 6a + 4b = 14 becomes 6 * 3/2 + 4b = 14 which becomes 9 + 4b = 14 solve for b in both equations to get: 4b = 14 - 9 which becomes 4b = 5 which becomes b = 5/4. you have: a = 3/2 and b = 5/4. replace a and b in your original equaiton to see if they are true. 3a + 2b = 7 becomes 3 * 3/2 + 2 * 5/4 = 7 which becomes 9/2 + 10/4 = 7 which becomes 18/4 + 10/4 = 7 which becomes 28/4 = 7 which becomes 7 = 7, confirming the values of a and b are good for the first equation. 8a + 4b = 17 becomes 8 * 3/2 + 4 * 5/4 = 17 which becomes 24/2 + 20/4 = 17 which becomes 48/4 + 20/4 = 17 which becomes 68/4 = 17 which becomes 17 = 17, confirming the value of a and b are good for the second equation. your solution is that plan A workout lasts 1.5 hours and plan B workout lasts 1.25 hours. let me know if you have any questions. theo
let a equal the the number of hours spent on plan A.
let b equal the number of hours spent on plan B.
that means the same value of a and b for both equations.
8a + 4b = 17
8a + 4b = 17
8a + 4b = 17 becomes 8 * 3/2 + 4b = 17 which becomes 12 + 4b = 17
4b = 17 - 12 which becomes 4b = 5 which becomes b = 5/4.
Question 1187827: A tunnel through a mountain is for a four-lane highway is to have a semi-
elliptical opening. The total width of the highway is to be 14.64m, and the
height of the edge of the road must be sufficient for a truck 3.56m high to
clear. If the height of the opening is 4.78metres,
i) Approximately how wide must the opening be?
ii)what will be the width of each lane if the barrier between the lanes is 0.6m?
Answer by Edwin McCravy(18960)
You can put this solution on YOUR website!
The semi-ellipse must be as above. We put the center at the origin. Since the height is 4.78 feet, the semi-minor axis = b = 4.78. The total width of the highway is 14.64 m, so each lane must be 7.32 m wide. For a truck 3.56 m high to just scrape the top of the tunnel, when its right side is at the edge of the highway, the ellipse must pass through the point (7.32,3.56), and also the point (-7.32,3.56). [Note: It would be more practical to make to make it a little higher, to go through a higher point so that an 3.56-m tall truck would have a little clearance and not scrape the top, but the problem didn't state any clearance, so I will allow the truck to scrape the top at the edge of the highway] The equation of an ellipse is
+
= 1 But since the center is (h,k) = (0,0), the equation simplifies to
+
= 1 We know that b = 4.78, so we have
+
= 1
+
= 1 Since it goes through the point (7.32,3.56), we substitute (x,y) = (7.32,3.56)
+
= 1
+
= 1 Solve that for "a" and get a = 10.969227733, the semi-major axis. The width of the opening must be the entire major axis, so the answer to your problem is twice that or 21.93845466 m.
ii)what will be the width of each lane if the barrier between the lanes is 0.6m? We will subtract half of 0.6 m, or 0.3 m from each lane. Then each lane will then be 7.32-0.3 = 7.02 m wide. Edwin
Question 1188053: In a certain restaurant, customers must pay Php 150 for the basic pizza
and Php 5 for each additional slice of meat topping they wish to have in
their pizza.Pam paid php225 for her pizza.How many slices of meat toppings were added to it?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(42255)
You can put this solution on YOUR website! The problem is so simple that the solution is in one line
. the number of slices is
=
= 15. ANSWER
Just solved.
Answer by Theo(11797)
You can put this solution on YOUR website! formula is: y = 5 * x + 150 y is the total price. when y = 225, the formula becomes 225 = 5 * x + 150 the number of additional slices of meat topping = 15. 150 + 5 * 15 = 150 + 75 = 225. solution is that 15 slices of meat topping were added to the basic slice.
customers pay 150 for the basic pizza and 5 for each additional slice of topping.
x is the number of additional slices of meat topping added.
subtract 150 from both sides of the equation to get:
75 = 5 * x
solve for x to get:
x = 75/5 = 15
this confirms the number of slices is correct.
Question 1187885: A tunnel throught mountain is for a four-lane highway is to have semi-ellitical opening. The total width of the highway is to be 14.64m, and the height of the opening is 4.78 metres.
¡ Aproximately how wide the opening be?
¡¡ What will be the width of each lane if the barrier between the lanes is 0.6m?
Answer by greenestamps(9979)
You can put this solution on YOUR website! I will guess that the problem is not presented correctly. With the questions that are asked, the fact that the tunnel cross section is semi-elliptical is irrelevant.... Furthermore, with only the given information, the two lanes closest to the edge of the tunnel will have zero height on their edges, which is absurd.... Nevertheless... to answer the questions that are asked.... i. The width of the tunnel is given: 14.64m. ii. With a total width of 14.64m, four lanes, and three barriers of 0.6m between lanes, the width available for the 4 lanes is 14.64-3(0.6) = 14.64-1.8 = 12.84m. That makes the width of each lane 12.84/4 = 3.21m. Since the picture drawn by that response is nonsensical, I suggest you re-post the problem presenting the information clearly and correctly.
Question 1188002: A bowling alley charges $8 for a game and an additional $2 per person for shoe rentals.
Use p to represent the number of people that pay for shoes.
Write an expression that shows the total cost to bowl a game.
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(67885)
You can put this solution on YOUR website!
A bowling alley charges $8 for a game and an additional $2 per person for shoe rentals.
Use p to represent the number of people that pay for shoes.
--------------------
How many can participate in a game?
How many will rent shoes?
----
Answer by MathLover1(19126)
Question 1187996: A phone company offers two monthly plans. Plan A costs $15 plus an additional $0.15 for each minute of calls. Plan B costs $26 plus an additional $0.13 for each minute of calls. For what amount of calling do the two plans cost the same?What is the cost when the two plans cost the same?
Answer by ikleyn(42255)
You can put this solution on YOUR website!
.
A phone company offers two monthly plans.
Plan A costs $15 plus an additional $0.15 for each minute of calls.
Plan B costs $26 plus an additional $0.13 for each minute of calls.
For what amount of calling do the two plans cost the same?
What is the cost when the two plans cost the same?
~~~~~~~~~~~~~~~~~~~ 15 + 0.15t = 26 + 0.13t (where t is the amount of calling time) From this equation t =
= 550 minutes. The common costs is 15 + 550*0.15 = 97.50 dollars.
Solved.
Question 1188004: There are 3 feeder bus services plying to and from the nearby town center. Ahmed can ride on one of these services or walk to the town center. However, he decides that on this way back , he will ride on one of these services. In how many ways can he go to the town center and back?
Answer by Solver92311(641)
You can put this solution on YOUR website! For each of the four ways he can get to town, there are three ways to get home, so 4 times 3. John
My calculator said it, I believe it, that settles it
From
I > Ø
Question 1187982: linda's family pays $132 for 8 baseball tickets plus parking, while Joaquin's family pays $90 for 5 baseball tickets plus parking. Which equation models the relation between the number of tickets bought x, and the total amount paid, y.
Answer by Boreal(14500)
You can put this solution on YOUR website!
132=8x+1P
90=5x+1P
subtract 2nd from first
42=3x
x=$14
P=$20 by substituting,
y=14x +Parking ($20)
Question 1187965: 6 Identical glass vases cost Rupees 7272.What is the cost of 1 glass vase?
Answer by Alan3354(67885)
You can put this solution on YOUR website!
6 Identical glass vases cost Rupees 7272. What is the cost of 1 glass vase?
---------------
To find $ per vase, divide the $ by the number of vases.
Question 1187922: A banquet hall charges a rental fee plus an additional charge for each guest. The total cost is $550 for 20 guests and $775 for 35 guests.
Find an equation to model the total cost, C, in terms of the number of guests, N.
Answer by greenestamps(9979)
You can put this solution on YOUR website! Informally.... The additional 35-20=15 guests cost an additional $775-$550=$225, so the cost per guest is $225/15 = $15. Since the cost for 20 guests is $550, the rental fee is $550-20($15)=$550-$300=$250. So the rental cost is a fee of $250 plus $15 per guest. Using formal algebra -- note that the calculations performed are exactly the same.... (x(1),y(1))=(20,550) The slope m (increase in cost (y) per guest (x)) is The equation is of the form ANSWER: The equation for the total cost C for N guests is
(x(2),y(2))=(35,775)
; and we know the slope m is 15. Plug in (x,y) = (20,550) to find b.
Question 1187890: A small firm manufactures and sells one liter cartons of non-alcoholic cocktails, "The Caribbean" and "Mr. Fruity", which sell for $1.00 and $1.25, respectively. Each is made by mixing fresh orange, pineapple, and apple juices in different proportions. "The Caribbean" consists of 1 part orange, 6 parts pineapple, and 1 part apple. "Mr. Fruity" consists of 2 parts orange, 3 parts pineapple, and 1 part apple. The firm can buy up to 300 L of orange juice, up to 1125 L of pineapple juice, and up to 195 L of apple juice each week at a cost of $0.74, $0.64, and $0.48 per liter, respectively. Find the number of cartons of the two drinks that the firm should produce in order to maximize profit.
Answer by Theo(11797)
You can put this solution on YOUR website! one carton of either drink is equal to 1 liter. the caribbean consists of 1 part orange juice, 6 parts pineapple juice, and 1 part apple juice. total number of parts for the caribbean is 8. since the total number of liters of each drink is 1, then: each part of the caribbean is 1/8 of 1 liter. since the caribbean consists of 1 part orange juice, 6 parts pineapple juice, and 1 part apple juice, then the caribbean uses 1/8 of a liter of orange juice, 6/8 of a liter of pineapple juice, 1/8 of a liter of apple juice. since mister fruity consists of 2 parts orange juice, 3 parts pineapple juice, and 1 part apple juice, then mister fruity uses 2/6 of a liter of orange juice, 3/6 of a liter of pineapple juice, 1/6 of a liter of apple juice. the firm can buy up to: 300 liters of orange juice, 1125 liters of pineapple juice, 195 liters of apple juice. since the caribbean uses 1/8 of a liter of orange juice and mister fruity uses 2/6 of a liter of orange juice, then your constraint equation for orange juice is: 1/8 * x + 2/6 * y <= 300 since the caribbean uses 6/8 of a liter of pineapple juice and mister fruity uses 3/6 of a liter of pineapple juice, then your constraint equation for pineapple is: 6/8 * x + 3/6 * y <= 1125 since the caribbean uses 1/8 of a liter of apple juice and mister fruity uses 1/6 of a liter of apple juice, then your constraint equation for apple juice is: 1/8 * x + 1/6 * y <= 195 another constraint is that both x and y must be greater than or equal to 0. the cost for orange juice is .74 per liter. the selling price of the caribbean is 1 dollar per liter. the profit equation is the selling price minus the cost. for the caribbean, the profit equation will be: for mister fruity, the profit equation will be: the profit equation is your objective function and is shown below: the constraint functions are: using the desmos.com calculator, you will graph the opposite of the inequalities. the corner points of the region of feasibility will contain the maximum profit. each of those corner points will be evaluated by the objective function to determine which of them contains the maximum profit. the coordinate points are in (x,y) format. the graph looks like this: all the constraints must be satisfied. x >= 0 and y >= 0 is satisfied. 1/8 * x + 2/6 * y <= 300 (orange juice) is satisfied because 1/8 * 720 + 2/6 * 630 = 300 which is equal to 300. 6/8 * x + 3/6 * y <= 1125 (pineapple juice) is satisfied because 720 * 6/8 + 3/6 * 630 = 855 which is less than 1125. 1/8 * x + 1/6 * y <= 195 (apple juice) is satisfied because 720 * 1/8 + 630 * 1/6 = 168.75 which is less than 195. if i did this right (always a consideration), your solution is that 720 cartons of the carribean and 630 cartons of mister fruity should be produced and sold to generate the maqximum profit.
let x = the number of liters of the caribbean.
let y = the number of liters of mister fruity.
mister fruity consists of 2 parts orange juice, 3 parts pineapple juice, and 1 part apple juice.
total number of parts for mister fruity is 6.
each part of mister fruity is 1/6 of 1 liter.
the cost for pineapple juice is .64 per liter.
the cost for apple juice is .48 per liter.
the selling price of mister fruity is 1.25 dollars per liter.
1.00 - 1/8 * .74 - 6/8 * .64 - 1/8 * .48 = .3675.
1.25 - 2/6 * .74 - 3/6 * .64 - 1/6 * .48 = .6033333333.
profit = .3675 * x + .6033333333 * y
1/8 * x + 2/6 * y <= 300 (orange juice)
6/8 * x + 3/6 * y <= 1125 (pineapple juice)
1/8 * x + 1/6 * y <= 195 (apple juice)
x >= 0
y >= 0
the area of the graph that is not shaded is your region of feasibility.
x represents the number of liters of the caribbean.
y represents the number of liters of mister fruity. 
Question 1187928: There are 19 animals in the field. Some are goats and some are ducks. There are 72 legs in all. How many of each animal are in the field?
Answer by ikleyn(42255)
You can put this solution on YOUR website! -------------- To see many other similar (and different) solved problems, look into the lessons
.
There are 19 animals in the field. Some are goats and some are ducks.
There are 72 legs in all. How many of each animal are in the field?
~~~~~~~~~~~~~~ Let x be the number of goats; then the number of ducks is (19-x). There is no need to remind that the ducs have two legs, while the goats have four legs. So we write an equation for the total of legs 4x + 2*(19-x) = 72. Simplify and find x 4x + 38 - 2x = 72 4x - 2x = 72 - 38 2x = 34 x = 34/2 = 17. ANSWER. There are 17 goats and 19-17 = 2 ducks. CHECK. 17*4 + 2*2 = 68 + 4 = 72 total legs. ! Correct !
Solved.
- Problem on two-wheel and three-wheel bicycles
- Problem on animals at a farm
- Problem on pills in containers
- What type of problems are these?
at this site.
Question 1187848: Given that the function f(x)= x/8 + 3/2x
(i) Determine the turning points of the graph
(ii) Determine the nature of the stationary points
(iii) Hence sketch the graph.
Answer by MathLover1(19126)
You can put this solution on YOUR website! substitute in turning points are at:
A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising).
(i)
to find them, derivate
'
equal to zero and solve for
.........cross multiply
=±
solutions:
or
or
(,
)
(,
)
(ii) Determine the nature of the stationary points
(,
)->Minimum
(,
)->Maximum
(iii)
Question 1187829: The temperature at which water freezes is 0ºC or 32ºF.The temperature at which water boils is 100ºC or 212ºF.
i) use degree Celsius as the dependendent variable to find the linear equation relates the two thermometers in a two-points form (X-X1)=m(Y-Y1) Draw a sketch that shows the linear relationship.
ii)Hence sketch their graph.
Answer by Theo(11797)
You can put this solution on YOUR website! you have two points. they are: (0,32) for the freezing point. the coordinate points are in (x,y) format. the slope intercept form of the linear equation is y = mx + b. the slope is the change in the value of y divided by the corresponding change in the value of x. the y-intercept is the value of y when the value of x = 0. let (0,32) be equal to (x1,y1) (x1,y1) is the freezing point. m = slope = (y2 - y1) / (x2 - x1) = (212 - 32) / (100 - 0) simplify this to get: m = slope = (y2 - y1) / (x2 - x1) = 180 / 100 = 1.8 the equation becomes y = 1.8 * x + b when x is equal to 0, y is equal to 32, therefore the y-intercept = b is equal to 32. the equation becomes y = 1.8 * x + 32. that's the linear relationship between celsius and fahrenheit, y being fahrenheit and x being celsius. that equation can be graphed as shown below. at the freezing point, celsius is 0 degrees (x) and fahrenheit is 32 degrees (y). at the boiling point, celsius is 100 degrees (x) and fahrenheit is 212 degrees. note that 1.8 is equivalent to 9/5. the formula becomes y = 9/5 * x + 32. you might be more familiar with the formula when 1.8 is expressed as 9/5.
the coordinate points are (x,y), where x is the temperature in celsius and y is the temperature in fahrenheit.
(100,212) for the boiling point.
x is the degrees in celsius.
y is the degrees in fahrenheit.
m is the slope
b is the y-intercept
let (100,212) be equal to (x2,y2)
(x2,y2) is the boiling point. 
Question 1187754: I add 7 to a certain number, I double the result, my final answer is 34. What was the number?
Answer by Alan3354(67885)
You can put this solution on YOUR website!
I add 7 to a certain number, I double the result, my final answer is 34. What was the number?
----------------
How much is it before you double it?
How much before you add 7?
Question 1187739: A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 2 tables is $18. The total cost to rent 3 chairs and 8 tables is $55. What is the cost to rent each chair and each table?
Answer by greenestamps(9979)
You can put this solution on YOUR website! Let c be the rental cost for each chair The total cost to rent 5 chairs and 2 tables is $18: 5c + 2t = 18 The total cost to rent 3 chairs and 8 tables is $55. 3c + 8t = 55 (1) Solving the problem informally, using logical reasoning.... Since the cost of 5 chairs and 2 tables is $18, the cost of 20 chairs and 8 tables is 4*$18 = $72. ANSWER: $1 per chair and $6.50 per table CHECK: (2) Using formal algebra.... 5c + 2t = 18 Multiply the first equation by 4: Compare that equation to the second original equation: Solve to find the cost for each chair: Use that cost per chair in the first original equation to find the cost per table: ANSWERS: c=1; t=6.5 -- i.e. $1 per chair and $6.50 per table Observe that the solution using formal algebra uses EXACTLY the same calculations as the informal solution. But we need to understand the formal algebraic solution, because an informal solution will not be possible when the problems get a lot more complicated.
Let t be the rental cost for each table
But the cost of 3 chairs and 8 tables is $55; the difference between the two cases is 20-3 = 17 more chairs for an additional $72-$55 = $17. So the rental cost for each chair is $17/17 = $1.
And then since 5 chairs at $1 each and 2 tables cost $18 to rent, the cost for the 2 tables is $13, so the cost per table is $6.50.
5c+2t = 5(1)+2(6.50) = 5+13 = 18
3c+8t = 3(1)+8(6.50) = 3+52 = 55
3c + 8t = 55
20c + 8t = 72
17c = 17
c = 17/17 = 1
5(1)+2t = 18
5+2t = 18
2t = 18-5 = 13
t = 13/2 = 6.5
Question 1187721: Mr. Agoncillo has at least Php 150, 000 deposited in two banks. One bank gives annual interest of 4% while the other bank gives 6%. In a year, Mr Agoncillo receives at most Php 12 000.
a. What mathematical statement represents the given situation?
Let x=
y=
Mathematical statement:
Answer by josgarithmetic(36654)
(Show Source): Question 1187700: In Canada, eastbound and westbound trains travel
along the same track, with sidings to pull onto to
avoid accidents. Two trains are now 150 miles apart,
with the westbound train traveling twice as fast as
the eastbound train. A warning must be issued to pu
one train onto a siding, or else the trains will crash in
1-1/4 hours. Find the speed of the eastbound train and
the speed of the westbound train.
Answer by Edwin McCravy(18960)
You can put this solution on YOUR website!
Two trains are now 150 miles apart,So Distance = 150
the westbound train traveling twice as fast as
the eastbound train.So let the eastbound train's rate is r. Then the westbound train's rate is 2r. Their approach rate is the sum of their rates, 3r
the trains will crash in 1-1/4 hours.So
So
DISTANCE = (RATE)(TIME)
The eastbound train's speed = r = 33 1/3 mph The westbound train's speed = 3r = 100 mph Edwin
Question 1187620: in a grocery store, each pound of poatoes of green beans cost one and a quartere times the price of each poud of potatoes. Mrs gomez bought 4 pounds of green beand and 5 pounds of potatoes misss jacobs bought 10 pounds of poatoes
Answer by ikleyn(42255)
Question 1187538: A group of graduating students rented a bus for their field trip for 6,000. 10 of the students withdraw from the trip and as a result the share of the others was increased by 20 pesos. How many were in the original field trip?
Answer by ikleyn(42255)
You can put this solution on YOUR website!
.
A group of graduating students rented a bus for their field trip for 6,000.
10 of the students withdraw from the trip and as a result the share of the others was increased by 20 pesos.
How many were in the original field trip?
~~~~~~~~~~~ Let n be the number of students originally. Write equation as you read the problem
-
= 20 pesos. To simplify, divide both sides by 20
-
= 1. From this point, you may guess the solution mentally: it is n = 60. Alternatively, you can reduce this equation to the standard quadratic form and solve it formally, using the quadratic formula or factoring. CHECK. I will check the original equation
-
=
-
= 120 - 100 = 20 pesos. ! Correct ! ANSWER. There were 60 students originally.
Solved.
Question 1187522: Donna baught a notebook for $3.50 and then spent half of her remaining money for a textbook. Next she baught sheet music for $4 and then spent half of the remaining money on a calculator. She has $8 left. How much money did she start with?
Answer by ikleyn(42255)
You can put this solution on YOUR website! It is a nice problem to solve it in the backward manner. Nice method, isn't it ?
.
Donna bought a notebook for $3.50 and then spent half of her remaining money for a textbook.
Next she bought sheet music for $4 and then spent half of the remaining money on a calculator.
She has $8 left. How much money did she start with?
~~~~~~~~~~~~~ Make the sheet of her purchases, step by step: 1. bought a notebook for $3.50 2. spent half of her remaining money for a textbook 3. bought the sheet music for $4. 4. spent half of the remaining money on a calculator. 5. she has $8 left. Now we will move from the bottom to the top. - before step 4, she had twice $8, i.e 16 dollars. - before step 3, sha had 16 + 4 = 20 dollars. - before step 2, she had twice $20, i.e. 40 dollars. - before step 1, she had 40 + 3.50 = 43.50 dollars. It is what she started with. You may check that my solution and my answer are correct at each step, moving from step 1 to the end.
Solved.
Question 1187516: A textbook store sold a combined total of 348 sociology and math textbooks in a week. The number of math textbooks sold was 64 less than the number of sociology textbooks sold. How many textbooks of each type were sold?
Answer by ikleyn(42255)
You can put this solution on YOUR website!
.
A textbook store sold a combined total of 348 sociology and math textbooks in a week.
The number of math textbooks sold was 64 less than the number of sociology textbooks sold.
How many textbooks of each type were sold?
~~~~~~~~~~~~~ Math + Sociology = 348 x + (x+64) = 348 2x = 348 - 64 = 284 x = 284/2 = 142. ANSWER. 142 Math textbooks and 142+64 = 206 Sociology textbooks.
Solved.
Question 1187447: The angles of a triangle are (2x+20)⁰,(x+25)⁰ and(2x−25)⁰ Given that the sum of the angles of a triangle is 180⁰, calculate the size of each angle
Answer by math_tutor2020(342)
(Show Source): You can put this solution on YOUR website! angle1+angle2+angle3 = 180 That x value then leads to... Note how: 84+57+39 = 180 to help confirm the correct answers ------------------------------------------------- Side note: This triangle is acute because all three angles are less than 90. The triangle is also scalene because the three angles are all different from each other.
As your teacher mentions, the three angles of any triangle add to 180.
(2x+20)+(x+25)+(2x-25) = 180
2x+20+x+25+2x-25 = 180
(2x+x+2x)+(20+25-25) = 180
5x+20 = 180
5x = 180-20
5x = 160
x = 160/5
x = 32
angle1 = 2x+20 = 2*32+20 = 64+20 =
angle2 = x+25 = 32+25 = 57 degrees
angle3 = 2x-25 = 2*32-25 = 64-25 = 39 degrees
angle1 = 2x+20 = 84 degrees
angle2 = x+25 = 57 degrees
angle3 = 2x-25 = 39 degrees
x = 32
Question 1187445: The temperature of a substance in an experiment changes by -7.5 Fahrenheit from 8 am to 2 pm. At 5 pm, the temperature is 43.5 Fahrenheit. It is 1/3 of what the temperature was at 2 pm. What was the temperature at 8 am of the substance?
Answer by greenestamps(9979)
You can put this solution on YOUR website! In the real world, the problem is nonsense. We are told that the temperature at 5pm, 43.5 degrees Fahrenheit, is 1/3 of what the temperature was at 2pm. It is nonsense to say one Fahrenheit temperature is 1/3 of another. It doesn't appear that the problem can be solved using any assumptions about what the actual information is; the rate of cooling between 2pm and 5pm is far greater than the rate between 8am and 2pm. The problem as posted makes no sense; it can't be solved.
Question 1187441: Alexis is x years old. Allie is 8 years older than Alexis. Five times Allie's age is equal to 180. How old is Alexis?
Answer by ikleyn(42255)
You can put this solution on YOUR website! Divide 180 by 5 and then subtract 8 from the quotient. Solved.
. = 28 years old.
Question 1187263: Lucy borrowed $80 from her friend in order to help buy a new video game system. Lucy agreed to pay back her friend $8 per week
write an equation representing the amount Lucy OWES her friend
I know the slope is -8 because she is paying back 8 dollars a week
y=-8x is that right? or would it be 80=-8x?
define the variables
**y axis I labeled amount owed
**x axis I labeled weeks
Found 2 solutions by MathTherapy, ikleyn:
Answer by MathTherapy(9934)
You can put this solution on YOUR website!
Lucy borrowed $80 from her friend in order to help buy a new video game system. Lucy agreed to pay back her friend $8 per week
write an equation representing the amount Lucy OWES her friend
I know the slope is -8 because she is paying back 8 dollars a week
y=-8x is that right? or would it be 80=-8x?
Your axes are labeled correctly. Your slope is also correct since every week, the $80 sum is DECREASED by $8.
As the amount owed is $80, the y-intercept is 80, and the line of the equation will slope downwards, since it's NEGATIVE.
The equation will then be .
Answer by ikleyn(42255)
Question 1187111: "A rectangle's 102 in perimeter is . Its length is 5 in longer than its width. Use an equation to find the rectangle's length and width." How do I set up the equation?
Answer by MathTherapy(9934)
You can put this solution on YOUR website!
"A rectangle's 102 in perimeter is . Its length is 5 in longer than its width. Use an equation to find the rectangle's length and width." How do I set up the equation?
Correct equations:
Reduce the 1st equation to get a simpler one.
Substitute the 2nd into the reduced version of the 1st and solve for W. Then find L, the length.
Question 1187240: I have no idea how to approach this, can you please help me.
The question is as followed,
Flying to Kampala with a tailwind a plane averaged 185 km/h. On the return trip the plane only averaged 143 km/h while flying back into the same wind. What is the speed of the wind and the speed of the plane while in the air?
They are asking me to write a linear equation and solve.
X= could represent the speed of the wind and Y=the speed of the plane while in the air.
not sure how to get the answer
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(42255)
Answer by Alan3354(67885)
You can put this solution on YOUR website!
Flying to Kampala with a tailwind a plane averaged 185 km/h. On the return trip the plane only averaged 143 km/h while flying back into the same wind. What is the speed of the wind and the speed of the plane while in the air?
They are asking me to write a linear equation and solve.
X= could represent the speed of the wind and Y=the speed of the plane while in the air.
not sure how to get the answer
=======================
The plane's airspeed is the average of the 2 groundspeeds.
= (185+143)/2 = 164 km/hr
================
Windspeed is the difference between airspeed and groundspeed.
164 - 143 = 21 km/hr
Question 1187243: y=-5/3x-1
y=x+7
Its asking to solve equation by graphing, then it ask for
X=?
Y=?
Found 3 solutions by Theo, josgarithmetic, Alan3354:
Answer by Theo(11797)
You can put this solution on YOUR website! the intersection point is at (x,y) = (12,19). that means y = 19 when x = 12. if you solve algebraically, you should get the same answer. algebraically, you would do the following: the two equatons that need to be solved simultaneously are: y=-5/3x-1 since they are both equal to y, then 5/3 * x - 1 must be equal to x + 7. you get: 5/3 * x - 1 = x + 7 subtract x from both sides of the equation and add 1 to both sides of the equation t0 get: 5/3 * x - x = 7 + 1 multiply both sides of this equation by 3 to get: 5 * x - 3 * x = 3 * (7 + 1) combine like terms and simplify to get: 2*x = 24. solve for x to get: x = 24/2 = 12. replace x in both original equations to get: y=-5/3x-1 becomes y = 5/3 * 12 - 1 = 20 - 1 = 19. the value of x is 12 in both equations and the value of y = 19 in both equations. both equations have been solved simultaneously by the value of x = 12 and y = 19. the graphical solution provided the same answer. that's because x = 12 when y = 19 is common to both equations which means it's also common to both lines on the graph created by those equations.
here's the graph. 
y=x+7
y=x+7 becomes y = 12 + 7 = 19.
Answer by josgarithmetic(36654)
(Show Source): You can put this solution on YOUR website! Now you can easily graph the two lines on the same coordinate system and identify the intersection point.
The two lines intersect at some point (x,y) which you can find, through graphing if you want or are told to.
vertical axis intercept is -1.
slope is .
Those read directly from the equation.
vertical axis intercept is 7.
slope is 1.
Those read directly from the equation.
Answer by Alan3354(67885)
You can put this solution on YOUR website!
y=-5/3x-1
y=x+7
------------
Use parentheses.
y= (-5/3)x-1
y=x+7
-----
Graph the 2 lines.
The intersection is x & y
Question 1187198: Admission prices in the bunawan variety shows where 20 pesos and fifty pesos the total cash in one of the ticket booth was 9550 tickets were sold to 320 people how many of each kind of tickets were sold
Answer by ikleyn(42255)
You can put this solution on YOUR website! It looks like a standard ticket problem. ---------------- It is a standard and typical tickets problem. There are different methods of solving such problems. From these lessons, learn on how to solve such problems once and for all. Also, you have this free of charge online textbook in ALGEBRA-I in this site The referred lessons are the part of this online textbook under the topic " Save the link to this online textbook together with its description Free of charge online textbook in ALGEBRA-I to your archive and use it when it is needed.
.
Admission prices in the bunawan variety shows where 20 pesos and fifty pesos
the total cash in one of the ticket booth was 9550 tickets were sold to 320 people
how many of each kind of tickets were sold
~~~~~~~~~~~~ You can start from the standard form equations x + y = 320 (1) 20x + 50y = 9550 (2) where x is the number of the 20-pesos tickets; y is the number of the 50-pesos tickets. Then you express x = 320-y from the first equation and substitute it into the second equation 20(320-y) + 50y = 9550 pesos. (3) Alternatively, you can start directly from equation (3) - it is up to you. From equation (3), y =
= 105. So, there are 105 50-peso tickets, and the rest (320-105) = 215 tickets are for 20 pesos. ANSWER CHECK. 50*105 + 20*215 = 9550 pesos, the total money. ! Correct !
Solved.
In this site, there are lessons
- Using systems of equations to solve problems on tickets
- Three methods for solving standard (typical) problems on tickets
explaining and showing all basic methods of solving such problems.
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
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Shawn Found That a Solution of X 3
Source: https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq