Let the number of books in the box be x.
It is given that the books in the box cost $300, it follows that each book will cost (in dollars):
[tex]\frac{300}{x}[/tex]Since 15 of the books were given to her brother, the number of books left is:
[tex]x-15[/tex]It is given that the books left were sold for $330 altogether. Hence, each of the books left was sold for:
[tex]\frac{330}{x-15}[/tex]It is also given that the profit made on each book sold is $1.5.
Recall that the profit is the difference between the selling price and the cost price.
Hence, equating the difference to the given profit gives:
[tex]\frac{330}{x-15}-\frac{300}{x}=1.5[/tex](Note that the cost price and selling price of each book was used since the profit given was for each book).
Next, solve the resulting equation for x:
[tex]\begin{gathered} \frac{330}{x-15}-\frac{300}{x}=1.5 \\ \text{Multiply through the equation with x(x-15):} \\ \Rightarrow x(x-15)\frac{330}{x-15}-x(x-5)\frac{300}{x}=x(x-5)1.5 \\ \text{Cancel out }common\text{ expressions}\colon \\ \Rightarrow x\cancel{(x-15)}\frac{330}{\cancel{(x-15)}}-\cancel{x}(x-15)\frac{300}{\cancel{x}}=x(x-15)1.5 \\ \Rightarrow330x-300(x-15)=x(x-15)1.5 \\ \Rightarrow330x-300x+4500=1.5x^2-22.5x \\ \Rightarrow30x+4500=1.5x^2-22.5x \\ \Rightarrow-1.5x^2+52.5x+4500=0 \end{gathered}[/tex]Solve the quadratic equation to get:
[tex]x=-40,75[/tex]Since x represents the number of books, discard the negative solution.
Hence, the number of books in the box is 75.
The original price of each book is given as:
[tex]\frac{300}{x}[/tex]Substitute x=75 into the expression:
[tex]\frac{300}{x}=\frac{300}{75}=\$4[/tex]Hence, the original price of each book is $4.
Answers:
The number of comic books in the box is 75.
The original price of each book is $4.