The U-Drive Rent-A-Truck company plans to spend $16 million on 320 new vehicles. Each commercial...

Question:

The U-Drive Rent-A-Truck company plans to spend $16 million on 320 new vehicles.

Each commercial van will cost $25,000, each small truck $80,000, and each large truck $70,000.

Past experience shows that they need twice as many vans as small trucks.

How many of each type of vehicle can they buy?

VANS
SMALL TRUCKS
LARGE TRUCKS

Proportion

A proportion is one of the mathematical equation that can be used to make comparison between the two values of ratios; that is, it is used to check that the two ratios are equal or not as (X/Y) = (W/Z) where the denominators y and z are not equal to zero.

Answer and Explanation:

Given Information

Let,

X be the numbers of Vans.

Y be the numbers of small trucks.

Z be the numbers of large trucks.

It is given that the company need twice as many vans as small trucks, which implies X = 2Y. The total numbers of vehicles required are 320.

The first equation is:

{eq}\begin{align*} X + Y + Z = 320\\ 2Y + Y + Z = 320\\ 3Y + Z = 320 \end{align*} {/eq}

The second equation is:

{eq}\begin{align*} &25000X + 80000Y + 70000Z = 16000000\\ &0.25\left( {2Y} \right) + 0.8Y + 0.7Z = 160\\ &1.3Y + 0.7Z = 160 \end{align*}{/eq}

Multiply the first equation by 0.7 and subtract equations:

{eq}\begin{align*} 2.1Y + 0.7Z = 224\\ 1.3Y + 0.7Z = 160\\ \\ 0.8Y = 64\\ Y = 80 \end{align*} {/eq}

And, Z = 80, X = 160

Therefore, the required numbers are as follow:

160 vans

80 small trucks

80 large trucks.


Learn more about this topic:

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What is a Proportion in Math? - Definition & Practice Problems

from High School Algebra I: Help and Review

Chapter 23 / Lesson 15
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