Word problem done with the Echelon method

Question

The U-Drive Rent-A-Truck company plans to spend $8 million on 280 new vehicles. Each commercial van will cost $25,000, each small truck $30,000, and each large truck $40,000. 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

Let the total number of vans be x, small trucks be y and large trucks be z.

 

So,

x + y + z = 280 -------- equation 1

 

25000v + 30000y + 40000z = 8000000 -------- equation 2

 

x = 2y -------- equation 3

 

Now insert equation 3 into 1

 

2y + y + z = 280

3y + z = 280

Lets make z the subject

z = 280 - 3y --------- equation 4

 

Finally insert equations 3 and 4 into 2

25000(2y) + 30000y + 40000(280 - 3y) = 8000000

Cancel out the zeros on either side

25(2y) + 30y + 40(280 - 3y) = 8000

50y + 30y + 11200 - 120y +800040y = 11200 - 8000

40y = 3200

y = 80 small trucks

 

Therefore

x = 2 x 80 = 160 vans

z = 280 - (3 x 80) = 40 large trucks