Fanny had some pencils, staplers and files. The ratio of the number of pencils to the number of staplers was 6 : 1. After giving away 30 staplers, the ratio of the number of files to the number of staplers was 3 : 1. Fanny bought another 180 files. As a result, there were an equal number of pencils and files. How many staplers did she have at first?
| |
Pencils |
Staplers |
Files |
| Before |
6 u |
1 u |
|
| Change |
|
- 30 |
|
| After 1 |
|
1 u - 30 |
3 u - 90 |
| Change |
|
|
+ 180 |
| After 2 |
6 u |
1 u - 30 |
3 u + 90 |
Number of staplers after Fanny gave away 30 staplers
= 1 u - 30
After Fanny gave away 30 staplers, the ratio of the number of files to the number of staplers became 3 : 1. This means that the number of staplers was 3 times as many as the number of files.
Number of files after Fanny gave away 30 staplers
= 3 x (1 u - 30)
= 3 u - 90
Number of files in the end after Fanny bought another 180 files
= 3 u - 90 + 180
= 3 u + 90
Number of pencils and files in the end is the same.
6 u = 3 u + 906 u - 3 u = 903 u = 90
1 u = 90 ÷ 3 = 30
Total numbers of staplers that Fanny had at first
= 1 u
= 30
Answer(s): 30
