Jane had some staplers, files and notebooks. The ratio of the number of staplers to the number of files was 7 : 1. After giving away 23 files, the ratio of the number of notebooks to the number of files was 4 : 1. Jane bought another 215 notebooks. As a result, there were an equal number of staplers and notebooks. How many files did she have at first?
| |
Staplers |
Files |
Notebooks |
| Before |
7 u |
1 u |
|
| Change |
|
- 23 |
|
| After 1 |
|
1 u - 23 |
4 u - 92 |
| Change |
|
|
+ 215 |
| After 2 |
7 u |
1 u - 23 |
4 u + 123 |
Number of files after Jane gave away 23 files
= 1 u - 23
After Jane gave away 23 files, the ratio of the number of notebooks to the number of files became 4 : 1. This means that the number of files was 4 times as many as the number of notebooks.
Number of notebooks after Jane gave away 23 files
= 4 x (1 u - 23)
= 4 u - 92
Number of notebooks in the end after Jane bought another 215 notebooks
= 4 u - 92 + 215
= 4 u + 123
Number of staplers and notebooks in the end is the same.
7 u = 4 u + 1237 u - 4 u = 1233 u = 123
1 u = 123 ÷ 3 = 41
Total numbers of files that Jane had at first
= 1 u
= 41
Answer(s): 41
