SOLUTION: The fast track company manufactures toy remote control race cars which it sells for $25 each the production costs for the company is $2100 per day plus $13 per race car how many ra

Question 1165704: The fast track company manufactures toy remote control race cars which it sells for $25 each the production costs for the company is $2100 per day plus $13 per race car how many race cars must they sell in one day to make a profit of $2700
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let c equal the total cost.
let r equal the total revenue.
let p = the profit which is equal to r - c.
let x equal the number of cars sold.

all figures are per day.
c = 13 * x + 2100
r = 25 * x
p = 25 * x - (13 * x + 2100) which is equal to 12 * x - 2100.

when p = 2700, the p formula becomes:
2700 = 12 * x - 2100
add 2100 to both sides of the equation to get:
4800 = 12 * x
solve for x to get:
x = 4800 / 12 = 400

when the number of cars sold is 400, they will make a profit of 2700 for the day.
to confirm, replace x with 400 in the equations.
r = 25 * x becomes r = 25 * 400 which becomes r = 10,000
c = 13 * x + 2100 wich becomes c = 13 * 400 + 2100 which becomes c = 5200 + 2100 which becomes c = 7300.
r - c becomes 10,000 - 7300 = 2700.

the value of x = 400 is confirmed to be good.
your solution is that they have to sell 400 cars to make 2700 profit.

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