Question

The​ U-Drive Rent-A-Truck company plans to spend ​$14 million on 280 new vehicles. Each commercial van will cost ​$55 comma 000​, each small truck ​$20 comma 000​, and each large truck ​$70 comma 000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they​ buy? They can buy nothing ​vans, nothing small​ trucks, and nothing large trucks.

Answer 1

Answer: They can buy 140 ​vans, 70​ small trucks, and 70 large trucks.

Explanation:

Let x represent the cost of each commercial van.

Let y represent the cost of each small truck.

Let z represent the cost of each large truck.

The total number if vehicles that they want to purchase is 280. It means that

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

Each commercial van will cost ​$55 000​, each small truck ​$20000​, and each large truck ​$70000. The total amount to be spent is $14000000. It means that

55000x + 20000y + 70000z = 14000000- - - - - - -2

Past experience shows that they need twice as many vans as small trucks. It means that

x = 2y

Substituting x = 2y into equation 1 and equation 2, it becomes

2y + y + z = 280

3y + z = 280

z = 280 - 3y - - - - - - - - -3

55000(2y) + 20000y + 70000z = 14000000

110000y + 20000y + 70000z = 14000000

130000y + 70000z = 14000000- - - - - - - 4

Substituting equation 3 into equation 4, it becomes

130000y + 70000(280 - 3y) = 14000000

130000y + 19600000 - 210000y = 14000000

130000y - 210000y = 14000000 - 19600000

- 80000y = -5600000

y = -5600000/- 80000

y = 70

x = 2y = 2 × 70

x = 140

z = 280 - 3y = 280 - 3(70)

z = 280 - 210

z = 70