Yen had some notebooks, pencils and files. The ratio of the number of notebooks to the number of pencils was 7 : 1. After giving away 30 pencils, the ratio of the number of files to the number of pencils was 5 : 1. Yen bought another 198 files. As a result, there were an equal number of notebooks and files. How many notebooks did she have at first?
| |
Notebooks |
Pencils |
Files |
| Before |
7 u |
1 u |
|
| Change |
|
- 30 |
|
| After 1 |
|
1 u - 30 |
5 u - 150 |
| Change |
|
|
+ 198 |
| After 2 |
7 u |
1 u - 30 |
5 u + 48 |
Number of pencils after Yen gave away 30 pencils
= 1 u - 30
After Yen gave away 30 pencils, the ratio of the number of files to the number of pencils became 5 : 1. This means that the number of pencils was 5 times as many as the number of files.
Number of files after Yen gave away 30 pencils
= 5 x (1 u - 30)
= 5 u - 150
Number of files in the end after Yen bought another 198 files
= 5 u - 150 + 198
= 5 u + 48
Number of notebooks and files in the end is the same.
7 u = 5 u + 487 u - 5 u = 482 u = 48
1 u = 48 ÷ 2 = 24
Total numbers of notebooks that Yen had at first
= 7 u
= 7 x 24
= 168
Answer(s): 168
