Question 1058097: The U-Drive Rent-A-Truck company plans to spend $16
million on 310
new vehicles. Each commercial van will cost $45000
,
each small truck $40000
,
and each large truck $80000
.
Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! Let C represent the number of commercial vans, S represent the number of small trucks, and L the number of large trucks.
Since the company intends to purchase 310 vehicles, you can write the following equation:
(Eq. 1) C + S + L = 310
The total cost of the vehicles is:
(Eq. 2) 45C + 40S + 80L = 16,000 (all values were divided by 1000 to keep the numbers small)
Then, since the number of commercial vans is twice the number of small trucks, you can write:
C = 2S
Substituting 2S in place of C in Eq. 1 and Eq. 2 gives the following equations:
2S + S + L = 310
45(2S) + 40S + 80L = 16,000
or
3S + L = 310
130S + 80L = 16,000
Multiplying the first of those equations by 80 gives the following system:
240S + 80L = 24,800
130S + 80L = 16,000
Subtracting the second equation from the first leaves:
110S = 8800
S = 80
Then:
C = 2S = 2(80) = 160
and
C + S + L = 310
160 + 80 + L = 310
L = 310 - 160 - 80
L = 70
Solution: The company should purchase 160 commercial vans, 80 small trucks, and 70 large trucks.
Check: The total cost would be:
45000(160) + 40000(80) + 80000(70) = 16,000,000
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