Answer:
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
