Emma had some staplers, files and notebooks. The ratio of the number of staplers to the number of files was 8 : 1. After giving away 29 files, the ratio of the number of notebooks to the number of files was 5 : 1. Emma bought another 202 notebooks. As a result, there were an equal number of staplers and notebooks. How many staplers did she have at first?
| |
Staplers |
Files |
Notebooks |
| Before |
8 u |
1 u |
|
| Change |
|
- 29 |
|
| After 1 |
|
1 u - 29 |
5 u - 145 |
| Change |
|
|
+ 202 |
| After 2 |
8 u |
1 u - 29 |
5 u + 57 |
Number of files after Emma gave away 29 files
= 1 u - 29
After Emma gave away 29 files, the ratio of the number of notebooks to the number of files became 5 : 1. This means that the number of files was 5 times as many as the number of notebooks.
Number of notebooks after Emma gave away 29 files
= 5 x (1 u - 29)
= 5 u - 145
Number of notebooks in the end after Emma bought another 202 notebooks
= 5 u - 145 + 202
= 5 u + 57
Number of staplers and notebooks in the end is the same.
8 u = 5 u + 578 u - 5 u = 573 u = 57
1 u = 57 ÷ 3 = 19
Total numbers of staplers that Emma had at first
= 8 u
= 8 x 19
= 152
Answer(s): 152
