If each large truck $70,000. Past experience shows that they need twice as many vans as small trucks. The number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.
<h3>How to find the number of vehicle?</h3>
Since the company intends to purchase 320 vehicle, Let write this equation:
C + S + L = 320 (Eq. 1)
Total cost of the vehicles:
25C + 80S +70L = 16,000 (Eq. 2) (Divided by 1000 to keep the numbers small)
Number of commercial vans is twice the number of small trucks,
C = 2S
Substituting 2S in place of C in Eq. 1 and Eq. 2
2S + S + L = 320
25(2S) +80S +70L = 16,000
130S + 70L = 16,000
Multiplying the first of those equations by 70
210S + 70L = 22,400
130S + 70L = 16,000
Subtracting the second equation from the first:
80S = 6400
Divide both side by 80S
S = 6400/80
S = 80 (Small truck)
Then:
C = 2S
C= 2(80)
C= 160 (Commercial van)
So,
C + S + L = 320
160 + 80 + L = 320
L = 320 - 160 - 80
L =80 (Large van)
Therefore the number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.
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