SOLUTION: 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 &#82

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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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