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.
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