Question

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 an internet website for $330 making a profit , making a profit of $1.50 on each one.how many comic books were in the box? what was the original price of each comic book (assuming they all cost the same amount)?​

Answer 1

Answer: There are 75 books.

Price of each book = $4.

Explanation:

Let x = Number of books in the box.

Then as per given,

Cost of x books = $300

Cost of one book =
`\$(\frac{300}x)`

Books left after giving 15 of them = x-15

Selling price of (x-15) books= $330

Selling price of one book =
`\$((330)/(x-15))`

Profit on each book= $1.50

Profit = selling price - cost price

`\Rightarrow 1.50=(330)/(x-15)-(300)/(x)\\\\\Rightarrow\ 1.50=(330(x)-300(x-15))/(x(x-15))\\\\\Rightarrow\ 1.50=(330x-300x+4500)/(x^2-15x)\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}]`

`\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75`

Number of books cannot be negative.

So, there are 75 books.

Price of each book =
`(300)/(75)=\$4`

So price of each book = $4.