Jada has read 3/5 of a book. She has read 75 pages so far. How many pages are in the whole book? Consider drawing a model to help you solve the problem.

\(75 \div \frac{3}{5} = 125\)

There are 125 pages in the whole book.

//

Proof:

\(125 \times \frac{3}{5} = 75\)

Answer:

125 pages

Step-by-step explanation:

I'll show you two ways to solve this problem. The first one uses an equation, and the second one uses a model like the problem suggests.

1) Solution using an equation:

The book has an unknown number of pages, so we call that unknown number x.

She read 3/5 of the pages of the book, so she read 3/5 of x.

We are told that 3/5 of x is 75.

We write an equation, and we solve it.

3/5 x = 75

Multiply both sides by the reciprocal of 3/5 which is 5/3.

5/3 * 3/5 x = 5/3 * 75

x = 125

Since we let x = the number of pages, then the answer is:

Answer: There are 125 in the book.

2) Solution using the drawing of a model

Below, each space of 10 dashes between 2 plus signs represents 1/5 of the book. There are 5 fifths in a unit, so there are 5 spaces of 10 dashes.

+----------+----------+----------+----------+----------+

    1/5          1/5        1/5         1/5         1/5

3/5 of the book is 3 of those spaces.

<-------------- 3/5 ------------>

+----------+----------+----------+----------+----------+

    1/5         1/5         1/5         1/5         1/5

We are told she read 3/5 of the book and that is 75 pages.

<-------------- 3/5 ------------>

<------------75 p ------------->

+----------+----------+----------+----------+----------+

    1/5         1/5         1/5         1/5         1/5

Since 3/5 of the book is 75 pages, 1/5 of the book is 1/3 of 75 pages. That means that each 1/5 of the book is 25 pages since 75/3 = 25.

   25 p       25 p      25 p     25 p      25 p

+----------+----------+----------+----------+----------+

    1/5         1/5         1/5         1/5         1/5

Since there are 5 fifths in 1 unit, there are 5 times 25 pages in the entire book.

5 * 25 pages = 125 pages.

This second solution was obtained by drawing a model instead of using an equation.

Answer: There are 125 pages in the book.

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