Question 1067595: A television weighs 50 pounds and a microwave weighs 30 pounds. A TV occupies 4 ft.³ and microwave occupies 3 ft.³. A truck is caring 1500 pounds of cargo that occupies 138 cubic feet of space. Which system of equations can be used to find the total number of televisions, t, microwaves, m, that is in the truck? Show your work
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! television weighs 50 pounds.
microwave weighs 30 pounds.
television occupies 4 cubic feet.
microwave occupies 3 cubit feet.
truck carries 1500 pounds of cargo.
truck occupies 138 cubic fee.
let T = number of televisions.
let M = number of microwaves.
50T + 30M = 1500 is your first equation.
4T + 3M = 138 is your second equation.
first equation addresses weight relationship.
second equation addresses space relationship.
if you solve these equations simultaneously, you should be able to find the number of televisions and microwaves that can be carried
solve as follows:
start with:
50T + 30M = 1500
4T + 3M = 138
multiply the second equation by 10 and leave the first equation as is to get:
50T + 30M = 1500
40T + 30M = 1380
subtract the second equation from the first to get:
10T = 120
solve for T to get T = 12
since 4T + 3M = 138, replace T with 12 to get:
4*12 + 3M = 138
simplify to get 48 + 3M = 138
subtract 48 from both sides of this equation to get 3M = 90
solve for M to get M = 30
you have T = 12 and M = 30
50T + 30M = 50*12 + 30*3 = 600 + 900 = 1500
4T+ 3M = 4*12 +3*30 = 48 + 90 = 138
both original equations are satisfied, so the solution looks good.
your solution is:
number of televisions is 12.
number of microwaves is 30.
|
|
|
