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?

50 large trucks, 90 small trucks, 180 vans

Step-by-step 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