Question

The​ U-Drive Rent-A-Truck company plans to spend ​$13 million on 320 new vehicles. Each commercial van will cost ​$25 comma 000​, each small truck ​$50 comma 000​, and each large truck  ​$80 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?

Answer 1

50 large trucks, 90 small trucks, 180 vans

Explanation:

This problem can be solved by setting up a system of equations and using substitution to solve for a variable. Given there are three types of vehicles, but that the number of vans is twice the number of small trucks, we can set up two variables:

large trucks = t, small trucks = s, commercial vans = 2s

The sum of all types of vehicles is 320: t + s + 2s = 320 or t + 3s = 320

The company can spend $13million and the cost of each vehicle is given:

80,000t + 50000s + 25000(2s) = 13,000,000

Combine like terms: 80,000t + 100,000s = 13,000,000

Use t = 320 - 3s to substitute for 't' in the second equation:

80,000(320 - 3s) + 100,000s = 13,000,000

25,600,000 - 240,000s + 100,000 = 13,000,000

-140,000s = -12,600,000 or s = 90

small trucks = 90, large trucks = 50 and commercial vans = 180