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.
