Joelle had some staplers, notebooks and pencils. The ratio of the number of staplers to the number of notebooks was 7 : 1. After giving away 24 notebooks, the ratio of the number of pencils to the number of notebooks was 5 : 1. Joelle bought another 220 pencils. As a result, there were an equal number of staplers and pencils. How many notebooks did she have at first?
| |
Staplers |
Notebooks |
Pencils |
| Before |
7 u |
1 u |
|
| Change |
|
- 24 |
|
| After 1 |
|
1 u - 24 |
5 u - 120 |
| Change |
|
|
+ 220 |
| After 2 |
7 u |
1 u - 24 |
5 u + 100 |
Number of notebooks after Joelle gave away 24 notebooks
= 1 u - 24
After Joelle gave away 24 notebooks, the ratio of the number of pencils to the number of notebooks became 5 : 1. This means that the number of notebooks was 5 times as many as the number of pencils.
Number of pencils after Joelle gave away 24 notebooks
= 5 x (1 u - 24)
= 5 u - 120
Number of pencils in the end after Joelle bought another 220 pencils
= 5 u - 120 + 220
= 5 u + 100
Number of staplers and pencils in the end is the same.
7 u = 5 u + 1007 u - 5 u = 1002 u = 100
1 u = 100 ÷ 2 = 50
Total numbers of notebooks that Joelle had at first
= 1 u
= 50
Answer(s): 50
