SOLUTION: A car rental company rents cars for $150 a day and vans for $300 a day. One day the total number of cars is 6 more than twice the number of vans and made $5700. How many cars and h

Question 1170208: A car rental company rents cars for $150 a day and vans for $300 a day. One day the total number of cars is 6 more than twice the number of vans and made $5700. How many cars and how many vans did the company sell on this day?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
c = number of cars
v = number of vans
cars cost 150 each and vans cost 300 each
total cost if 5700
equation is:
150c + 300v = 5700
you are given that the number of cars rented is 6 more than twice the number of vans rented.
the equation for that is:
c = 2v + 6
in the equation of 150c + 300v = 5700, replace c with 2v + 6 to get:
150 * (2v + 6) + 300v = 5700
simplify to get:
300v + 900 + 300v = 5700
subtract 900 from both sides of the equation and combine like terms to get:
600v = 4800
solve for v to get:
v = 8
replace v with 8 in the equation of 150c + 300v = 5700 and simplify to get:
150c + 2400 = 5700
subtract 2400 from both sides of the equation to get:
150c = 3300
solve for c to get:
c = 3300/150 = 22
you have 22 cars and 8 vans that are rented that day for a total of 5700.
22 * 150 + 8 * 300 = 3300 + 2400 = 5700
this confirms the number of cars and vans are good.
your solution is that they rented 22 cars and 8 vans that day.

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