Question

The​ U-Drive Rent-A-Truck company plans to spend ​$88 million on 280280 new vehicles. Each commercial van will cost ​$25 comma 00025,000​, each small truck ​$30 comma 00030,000​, and each large truck ​$40 comma 00040,000. 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

400

Step-by-step explanation:

The computation is shown below:-

x = commercial vans

y = small trucks

z = large trucks

Therefore

x + y + z = 280 ........................ (i)

Given that

x = 2y .....................(ii)

Now

$25,000 x + $30,000 y + $40,000 z = $88,000,000 ................ (iii)

We know x = 2y already,

so in the first equation:

2y + y + z = 280

3y + z = 280

x = 280 - 3y

So, we will use this in the third equation

$25,000(2y) + $30,000y + $80,000(280-3y) = $88,000,000

$50,000y + $30,000y + $22,400,000 - $240,000y = $88,000,000

-$160,000y = -$65,600,000

y = 410

Putting in 410 in the second equation:

x = 2 × 410

= 810

and finally

= x - y

= 810 - 410

= 400