Yen had some staplers, pens and files. The ratio of the number of staplers to the number of pens was 6 : 1. After giving away 19 pens, the ratio of the number of files to the number of pens was 4 : 1. Yen bought another 180 files. As a result, there were an equal number of staplers and files. How many staplers did she have at first?
| |
Staplers |
Pens |
Files |
| Before |
6 u |
1 u |
|
| Change |
|
- 19 |
|
| After 1 |
|
1 u - 19 |
4 u - 76 |
| Change |
|
|
+ 180 |
| After 2 |
6 u |
1 u - 19 |
4 u + 104 |
Number of pens after Yen gave away 19 pens
= 1 u - 19
After Yen gave away 19 pens, the ratio of the number of files to the number of pens became 4 : 1. This means that the number of pens was 4 times as many as the number of files.
Number of files after Yen gave away 19 pens
= 4 x (1 u - 19)
= 4 u - 76
Number of files in the end after Yen bought another 180 files
= 4 u - 76 + 180
= 4 u + 104
Number of staplers and files in the end is the same.
6 u = 4 u + 1046 u - 4 u = 1042 u = 104
1 u = 104 ÷ 2 = 52
Total numbers of staplers that Yen had at first
= 6 u
= 6 x 52
= 312
Answer(s): 312
