Fanny had some pens, staplers and files. The ratio of the number of pens to the number of staplers was 7 : 1. After giving away 21 staplers, the ratio of the number of files to the number of staplers was 4 : 1. Fanny bought another 168 files. As a result, there were an equal number of pens and files. How many pens did she have at first?
| |
Pens |
Staplers |
Files |
| Before |
7 u |
1 u |
|
| Change |
|
- 21 |
|
| After 1 |
|
1 u - 21 |
4 u - 84 |
| Change |
|
|
+ 168 |
| After 2 |
7 u |
1 u - 21 |
4 u + 84 |
Number of staplers after Fanny gave away 21 staplers
= 1 u - 21
After Fanny gave away 21 staplers, the ratio of the number of files to the number of staplers became 4 : 1. This means that the number of staplers was 4 times as many as the number of files.
Number of files after Fanny gave away 21 staplers
= 4 x (1 u - 21)
= 4 u - 84
Number of files in the end after Fanny bought another 168 files
= 4 u - 84 + 168
= 4 u + 84
Number of pens and files in the end is the same.
7 u = 4 u + 847 u - 4 u = 843 u = 84
1 u = 84 ÷ 3 = 28
Total numbers of pens that Fanny had at first
= 7 u
= 7 x 28
= 196
Answer(s): 196
