Past experience shows that they need twice as many sans as small trucks. How many of each type of vehicle can they buy?

Question

The U-Drive Rent-A-Truck company plans to spend $14 million on 280 new vehicles. Each commercial van will cost $55,000, each small truck $20,000, and each large truck $70,000. Past experience shows that they need twice as many sans as small trucks. How many of each type of vehicle can they buy?

Answer 1

Hi Shelby,

 

Let x = # of vans

Let y = # of small trucks

Let z = # of large trucks

 

x = 2y (need twice as many van as small trucks

 

x + y + z =280

 

55000(x) + 20000(y) + 70000z = 14000000

 

divide by 1000 to make it a little easier

 

55x + 20y + 70Z = 14000

 

now repalce x with 2y in both equations

 

2y + y + z = 280

55(2y) + 20y + 70z = 14000

 

3y + z = 280

130y + 70z = 14000

 

multiply the first equation by 70 and subtract equations

 

210y + 70z = 19600

130y + 70z = 14000

 

80y = 5600

y = 70         (70 small trucks

 

x = 2y          (140 vans

 

z = 280 - x - y  = 70   (large trucks

 

you can multiply the numbers by the cost to see that you spend 14 million but it does check out

 

Hope this helps