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7 December, 05:47

The u-drive rent-a-truck company plans to spend $10 million on 260 new vehicles. each commercial van will cost $25 comma 000 , each small truck $50 comma 000 , and each large truck $50 comma 000. past experience shows that they need twice as many vans as small trucks. how many of each type of vehicle can they buy?

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  1. 7 December, 05:49
    0
    Answer: 120 commercial vans, 60 small trucks, and 80 large trucks

    Explanation: First, we will define the variables that we need to solve the problem. In this case the question is, how many of each type of vehicle, so let

    V = number of vans

    S = number of small trucks

    L = number of large trucks

    Next, we will translate the words in the problem into mathematical statements that we can use to solve the problem, thus:

    "twice as many vans as small trucks" means that:

    V = 2*S

    "260 new vehicles" means that:

    V + S + L = 260

    The last part is the cost equation which is a little more complicated:

    25000*V + 50000*S + 50000*L = 10,000,000

    Divide both sides of this equation by 1000, we have:

    25*V + 50*S + 50*L = 10000

    We start with the simplest one:

    V = 2*S.

    This means that wherever we see a V in the other 2 equations we can replace it with 2*S, which will leave us with 2 equations in 2 unknowns

    (2*S) + S + L = 260 = => 3*S + L = 260

    25 * (2*S) + 50*S + 50*L = 10000

    ==> 100*S + 50*L = 10000

    Now we can solve the top equation for L to get L = 260 - 3*S

    and substitute this value for L into the bottom equation

    100*S + 50 * (260 - 3*S) = 10000

    100*S + 13000 - 150*S = 10000

    -50*S = - 3000

    S = 60

    Once we have one of the answers then plug in back in to previous equations to find the others

    L = 260 - 3*S = 260 - 3 * (60)

    = 260 - 180 = 80

    V = 2*S = 2 * (60) = 120

    So they can buy 120 commercial vans, 60 small trucks, and 80 large trucks
  2. 7 December, 06:09
    0
    Answer: They would buy 130 vans, 65 small trucks and 65 large trucks

    Explanation: Budget has been given as $10,000 and the company needs up to 260 vehicles, commercial vans ($25000), small trucks ($50000) and large trucks ($50000). They need twice as many vans as small trucks which means for every small truck purchased, they would purchase two commercial vans, or ratio 2:1 for the ratio of commercial vans to small trucks. The cost of the small truck is the same as the cost of the large truck. Therefore the ratio would be 2:1:1, for the ratio of commercial vans to small trucks to large trucks.

    The number of commercial vans to be purchased therefore is derived as

    2/4 = x/260

    (2 x 260) / 4 = x

    520/4 = x

    130 = x

    The number of vans to be purchased is 130 and this is twice the number of small trucks which means small trucks purchased would be 130 divided by 2 which equals 65, and large trucks also would be 65 making a total of 260 vehicles.
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