The u-drive rent-a-truck company plans to spend $8 million on 280 new vehicles. Each commercial van will cost $25,000, each small truck $30,000, and large truck $40,000. Past experience shows that they need twice as many vans as small truck. How many of each type of vehicle can they buy?

Question

Mathematics

Koen Rush

25 December, 04:24

The u-drive rent-a-truck company plans to spend $8 million on 280 new vehicles. Each commercial van will cost $25,000, each small truck $30,000, and large truck $40,000. Past experience shows that they need twice as many vans as small truck. How many of each type of vehicle can they buy?

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Answers (1)

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Mario Monroe · Answer 1

They can buy 160 commercial vans, 80 small trucks and 40 large trucks.

Step-by-step explanation:

The company plans to spend $8 million on 280 new vehicles.

Commercial van = $25,000

Small truck = $30,000

Large Truck = $40,000

Let 'x' be commercial van, 'y' small truck and 'z' large truck. Therefore:

x + y + z = 280

Also, we know that x = 2y

Therefore: 3y + z = 280

Also we know that:

25,000x + 30,000y + 40,000z = 8,000,000

50,000y + 30,000y + 40,000z = 8,000,000

80,000y + 40,000z = 8,000,000

Therefore, we need to solve the following system of equation:

3y + z = 280 [1]

80,000y + 40,000z = 8,000,000 [2]

We have that the results are: y=80, z=40 and x=160.

Therefore, they can buy 160 commercial vans, 80 small trucks and 40 large trucks.