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?

They can buy 160 commercial vans, 80 small trucks and 40 large trucks.

Step-by-step explanation:

The company plans to spend $8 million on 280 new vehicles.

Commercial van = $25,000

Small truck = $30,000

Large Truck = $40,000

Let 'x' be commercial van, 'y' small truck and 'z' large truck. Therefore:

x + y + z = 280

Also, we know that x = 2y

Therefore: 3y + z = 280

Also we know that:

25,000x + 30,000y + 40,000z = 8,000,000

50,000y + 30,000y + 40,000z = 8,000,000

80,000y + 40,000z = 8,000,000

Therefore, we need to solve the following system of equation:

3y + z = 280 [1]

80,000y + 40,000z = 8,000,000 [2]

We have that the results are: y=80, z=40 and x=160.

Therefore, they can buy 160 commercial vans, 80 small trucks and 40 large trucks.