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 large truck $40,000. Past experience shows that they need twice as many vans as small truck. How many of each type of vehicle can they buy?

Answer 1

1 large truck, 99 small trucks and 180 commercial vans

Explanation:

Step 1 : Write the data.

Total amount: 8,000,000

Total trucks needed: 280

Cost of commercial van (x) = $25,000

Cost of small truck (y) = $30,000

Large truck = $40,000 (from my understanding, only 1 large truck has to be bought since the amount given for commercial vans and small trucks is for each of it.

Since they need twice as many vans as small trucks, commercial van will be 2y and small truck will be y

Step 2 : Form two equations

40,000 + 25000(x) + 30000(y) = 8,000,000

25000(x) + 30000(y) = 7960,000 (equation 1)

1(large truck) + x + y =280

x + y = 279 (equation 2)

Step 3 : Find the value of y

From equation 2:

x = 279 - y

From equation 1:

25000(x) + 30000(y) = 7960,000

25000(279 - y) + 30000(y) = 7960,000

-25000y + 30000y + 6975000 = 7960000

5000y = 985000

y= 98.5 rounded off to 99 small trucks

Step 4: Find value of x

x + y = 279

y = 279 - 99

y = 180 commercial vans

Step 5: Answer how many type of each vehicle can they buy.

They can buy:

1 large truck

99 small trucks

180 commercial vans

!!