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)?
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!
To solve this problem, let's break it down step by step:
1. Let's start by finding out how many comic books Marco sold on the internet. We know that he gave 15 comic books to his brother, so the number of comic books he sold is equal to the total number of comic books minus 15.
Let's represent the total number of comic books in the box as "x". Therefore, the number of comic books Marco sold is x - 15.
2. We also know that Marco made a profit of $1.50 on each comic book he sold. So, the total profit he made from selling the comic books is equal to the number of comic books sold multiplied by the profit per comic book.
The total profit from selling the comic books is equal to (x - 15) * $1.50 = $330.
3. Now, let's set up an equation to solve for "x", the total number of comic books in the box:
(x - 15) * $1.50 = $330
4. Let's solve for "x" by dividing both sides of the equation by $1.50:
x - 15 = $330 / $1.50
x - 15 = 220
5. Now, let's isolate "x" by adding 15 to both sides of the equation:
x = 220 + 15
x = 235
Therefore, there were 235 comic books in the box.
6. Finally, let's find the original price of each comic book. We know that Marco purchased the entire box of comic books for $300. So, the original price of each comic book is equal to the total cost divided by the total number of comic books:
Original price per comic book = $300 / 235
Original price per comic book ≈ $1.28
Therefore, the original price of each comic book was approximately $1.28.