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20 April, 06:32

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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  1. 20 April, 07:32
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    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.
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