Fanny had some notebooks, pens and files. The ratio of the number of notebooks to the number of pens was 8 : 1. After giving away 23 pens, the ratio of the number of files to the number of pens was 5 : 1. Fanny bought another 202 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 |
8 u |
1 u |
|
Change |
|
- 23 |
|
After 1 |
|
1 u - 23 |
5 u - 115 |
Change |
|
|
+ 202 |
After 2 |
8 u |
1 u - 23 |
5 u + 87 |
Number of pens after Fanny gave away 23 pens
= 1 u - 23
After Fanny gave away 23 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 Fanny gave away 23 pens
= 5 x (1 u - 23)
= 5 u - 115
Number of files in the end after Fanny bought another 202 files
= 5 u - 115 + 202
= 5 u + 87
Number of notebooks and files in the end is the same.
8 u = 5 u + 878 u - 5 u = 873 u = 87
1 u = 87 ÷ 3 = 29
Total numbers of pens that Fanny had at first
= 1 u
= 29
Answer(s): 29