Asked by Julia
Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on the internet for $330, making a profit of $1.50 on each one. How many comic books were in the box? What was the original price of each comics book (assuming they all cost the same amount)?
Answers
Answered by
Reiny
number of comic books he bought --- x
cost price per comic = 300/x
number sold = x-15
selling price of each comic = 330/(x-15)
330/(x-15) - 300/x = 1.50 = 3/2
multiply each term by 2x(x-15)
660x - 600(x-15) = 3x(x-15)
660x - 600x + 9000 = 3x^2 - 45x
3x^2 - 105x - 9000 = 0
x^2 - 35x - 3000 = 0
(x + 40)(x - 75) = 0
x = 75 or a negative, which we reject
He bought 75 comic books at $4.00 each
check: 75*4 = 300 , check!
60*5.5 = 330, check!
cost price per comic = 300/x
number sold = x-15
selling price of each comic = 330/(x-15)
330/(x-15) - 300/x = 1.50 = 3/2
multiply each term by 2x(x-15)
660x - 600(x-15) = 3x(x-15)
660x - 600x + 9000 = 3x^2 - 45x
3x^2 - 105x - 9000 = 0
x^2 - 35x - 3000 = 0
(x + 40)(x - 75) = 0
x = 75 or a negative, which we reject
He bought 75 comic books at $4.00 each
check: 75*4 = 300 , check!
60*5.5 = 330, check!