Min had some notebooks, pens and files. The ratio of the number of notebooks to the number of pens was 7 : 1. After giving away 15 pens, the ratio of the number of files to the number of pens was 5 : 1. Min bought another 181 files. As a result, there were an equal number of notebooks and files. How many pens did she have at first?
| |
Notebooks |
Pens |
Files |
| Before |
7 u |
1 u |
|
| Change |
|
- 15 |
|
| After 1 |
|
1 u - 15 |
5 u - 75 |
| Change |
|
|
+ 181 |
| After 2 |
7 u |
1 u - 15 |
5 u + 106 |
Number of pens after Min gave away 15 pens
= 1 u - 15
After Min gave away 15 pens, the ratio of the number of files to the number of pens became 5 : 1. This means that the number of pens was 5 times as many as the number of files.
Number of files after Min gave away 15 pens
= 5 x (1 u - 15)
= 5 u - 75
Number of files in the end after Min bought another 181 files
= 5 u - 75 + 181
= 5 u + 106
Number of notebooks and files in the end is the same.
7 u = 5 u + 1067 u - 5 u = 1062 u = 106
1 u = 106 ÷ 2 = 53
Total numbers of pens that Min had at first
= 1 u
= 53
Answer(s): 53
