SOLUTION: The​ U-Drive Rent-A-Truck company plans to spend ​$16
million on 310
new vehicles. Each commercial van will cost ​$45000
​,
each small truck R
Algebra.Com
Question 1058097: The U-Drive Rent-A-Truck company plans to spend $16
million on 310
new vehicles. Each commercial van will cost $45000
,
each small truck $40000
,
and each large truck $80000
.
Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?
Answer by solve_for_x(190) (Show Source): You can put this solution on YOUR website!
Let C represent the number of commercial vans, S represent the number of small trucks, and L the number of large trucks.
Since the company intends to purchase 310 vehicles, you can write the following equation:
(Eq. 1) C + S + L = 310
The total cost of the vehicles is:
(Eq. 2) 45C + 40S + 80L = 16,000 (all values were divided by 1000 to keep the numbers small)
Then, since the number of commercial vans is twice the number of small trucks, you can write:
C = 2S
Substituting 2S in place of C in Eq. 1 and Eq. 2 gives the following equations:
2S + S + L = 310
45(2S) + 40S + 80L = 16,000
or
3S + L = 310
130S + 80L = 16,000
Multiplying the first of those equations by 80 gives the following system:
240S + 80L = 24,800
130S + 80L = 16,000
Subtracting the second equation from the first leaves:
110S = 8800
S = 80
Then:
C = 2S = 2(80) = 160
and
C + S + L = 310
160 + 80 + L = 310
L = 310 - 160 - 80
L = 70
Solution: The company should purchase 160 commercial vans, 80 small trucks, and 70 large trucks.
Check: The total cost would be:
45000(160) + 40000(80) + 80000(70) = 16,000,000
RELATED QUESTIONS
A truck can be rented from Company A for $70 a day plus $0.60 per mile.... (answered by jorel1380)
A truck can be rented from Company A for $70 a day plus $0.60 per mile.... (answered by ankor@dixie-net.com)
A truck can be rented from Company A for $70 a day plus $0.20 per mile.... (answered by josgarithmetic)
A company paid $150,000 for a new 18-wheeler. When it is 9 years old it... (answered by josgarithmetic)
An investment group is renovating a commercial building and will rent offices to small... (answered by solve_for_x)
Esmeralda invested $46004600 in two stock plans. On one, the risky... (answered by ikleyn)
Moving van rentals : Stringer Truck Rentals will rent a moving van for $15.75/day plus... (answered by stanbon)
A company markets exercise DVDs that sell for $14.95, including shipping and... (answered by ankor@dixie-net.com)
A company is considering two insurance plans with coverage and premiums shown in the... (answered by lawson221)