Jean had some staplers, notebooks and files. The ratio of the number of staplers to the number of notebooks was 6 : 1. After giving away 30 notebooks, the ratio of the number of files to the number of notebooks was 4 : 1. Jean bought another 206 files. As a result, there were an equal number of staplers and files. How many notebooks did she have at first?
| |
Staplers |
Notebooks |
Files |
| Before |
6 u |
1 u |
|
| Change |
|
- 30 |
|
| After 1 |
|
1 u - 30 |
4 u - 120 |
| Change |
|
|
+ 206 |
| After 2 |
6 u |
1 u - 30 |
4 u + 86 |
Number of notebooks after Jean gave away 30 notebooks
= 1 u - 30
After Jean gave away 30 notebooks, the ratio of the number of files to the number of notebooks became 4 : 1. This means that the number of notebooks was 4 times as many as the number of files.
Number of files after Jean gave away 30 notebooks
= 4 x (1 u - 30)
= 4 u - 120
Number of files in the end after Jean bought another 206 files
= 4 u - 120 + 206
= 4 u + 86
Number of staplers and files in the end is the same.
6 u = 4 u + 866 u - 4 u = 862 u = 86
1 u = 86 ÷ 2 = 43
Total numbers of notebooks that Jean had at first
= 1 u
= 43
Answer(s): 43
