Question

The U-Drive Rent-A-Truck company plans to spend $8 million in 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

solution:

we will use the equation system to solve this problem

explanation step by step:

There are three types of vehicles, and it is said that the number of vans is twice the number of small trucks.

let t denots the truck , S denote the small truck

and van = 2S....(because vans are twice than small truck)

total vehicle plans to buy = 280

we can formulate the equation as

T + S + 2S = 280

T + 3S = 280.............equation i

the company plans to spend $ 8 million on these vhicles

the cost of each vehicle is given by

van cost =$25000, small truck cost = $30,000 and large truck =$40,000

so formulate the second equation we get

40,000T + 30,000S + 25,000(2S) = 8,000,000

by solving this equation we get

40,000T + 80,000S = 8,000,000...............equation ii)

from equi i we get

T = 280-3s

putting value of t in equitaion 11

we get ,

40,000(280-3S) + 80,000 S = 8,000,000

by solving equation we get

S = 80

putting value of s in equation i we get

T = 280-3(80)

T = 40

so number of vehicle to purchase are

so number of van = 2*80 = 160

small truck = 80

large truck = 40