Question 1201031: Formulate but do not solve the problem.
The management of Hartman Rent-A-Car has allocated $2.16 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $16,000 each, intermediate-size cars cost $24,000 each, and full-size cars cost $32,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Let x, y, and z denote the number of compact, intermediate-sized, and full-size cars purchased, respectively.)
?= 2,160,000
?= x
?= 100
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a = numbr of compact cars
b = number of intermediate size cars.
c = number of full size cars.
we'll work in thousands.
16,000 = 16
24,000 = 24
31,000 = 32
2.16 million = 2,160,000 = 2160
a + b + c = 100
16a + 24b + 32c = 2160
since a = 2b, you can replace a with 2b in the equations to get:
2b + b + c = 100
16*2b + 24b + 31c = 2160
simplify and combine like terms to get:
3b + c = 100
56b + 32c = 2160
these are 2 equations that need to be solved simultaneously that you can then use to solve for b and c.
from that, you can then solve for a.
when you solve this, you should get a = 52, b = 26, c = 22, all in thousands.
that results in 52 * 16000 + 26 * 24000 + 22 * 32000 = 2,160,000.
let me know if you have any trouble doing that.
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