Question

The U-dnve Rent-a-truck company Plans to SPend 16 million on 320 new vehicles, Each commercial van will Cost 25,000 , each Small truck $ 80,000 , and each larg truck $70,00 o, Past experien ce Shows that they need twice as many vans.as Small trucks, How many of each type of vehicle can they buyn and -lage trucks. vans, - small trucks can buy They

Answer 1

Let the number of vans be x, number of small trucks be y and number of large trucks be z.

Then, according to question, total new vehicles, x+y+z=320.......(1)

Also,the company plans to spend 16 millions in total on all vehicles. Given the cost of vehicles, the sum of money spend on all new vehicles must be 16 million.

Thus, 25,000x + 80,000y+70,000z= 16,000,000

By simplyfying, we get,

25x+80y+70z=16,000..........(2)

The company needs twice as many vans as small trucks. Thus, number of vans must be twice that of small trucks.

Thus, x=2y....(3)

Solving the three equations 1,2&3,we get the answer.

Putting three in 1,we have x+y+z=320 => 2y+y+z=320 =>3y+z=320 => z= 320 - 3y

Putting this in 2,we have

25(2y)+80y+70(320-3y)=16,000

50y+80y+22400-210y=16000

-80y= - 6400

y=6400/80= 80

x= 2y=2*80=160

z= 320 - 3*80=320 - 240= 80

Thus, the company buys 160 vans, 80 small trucks and 80 large trucks.