Victorium had some files, pens and staplers. The ratio of the number of files to the number of pens was 6 : 1. After giving away 21 pens, the ratio of the number of staplers to the number of pens was 3 : 1. Victorium bought another 153 staplers. As a result, there were an equal number of files and staplers. How many pens did she have at first?
| |
Files |
Pens |
Staplers |
| Before |
6 u |
1 u |
|
| Change |
|
- 21 |
|
| After 1 |
|
1 u - 21 |
3 u - 63 |
| Change |
|
|
+ 153 |
| After 2 |
6 u |
1 u - 21 |
3 u + 90 |
Number of pens after Victorium gave away 21 pens
= 1 u - 21
After Victorium gave away 21 pens, the ratio of the number of staplers to the number of pens became 3 : 1. This means that the number of pens was 3 times as many as the number of staplers.
Number of staplers after Victorium gave away 21 pens
= 3 x (1 u - 21)
= 3 u - 63
Number of staplers in the end after Victorium bought another 153 staplers
= 3 u - 63 + 153
= 3 u + 90
Number of files and staplers 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 pens that Victorium had at first
= 1 u
= 30
Answer(s): 30
