Question

I need help for this question, because I didn't understand. Could you please clearly explain me please?

Answer 1

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):

`(300)/(x)`

Since 15 of the books were given to her brother, the number of books left is:

`x-15`

It is given that the books left were sold for $330 altogether. Hence, each of the books left was sold for:

`(330)/(x-15)`

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:

`(330)/(x-15)-(300)/(x)=1.5`

(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:

`\begin{gathered} (330)/(x-15)-(300)/(x)=1.5 \\ \text{Multiply through the equation with x(x-15):} \\ \Rightarrow x(x-15)(330)/(x-15)-x(x-5)(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}`

Solve the quadratic equation to get:

`x=-40,75`

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:

`(300)/(x)`

Substitute x=75 into the expression:

`(300)/(x)=(300)/(75)=\$4`

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.