Victorium had some staplers, notebooks and pens. The ratio of the number of staplers to the number of notebooks was 8 : 1. After giving away 15 notebooks, the ratio of the number of pens to the number of notebooks was 5 : 1. Victorium bought another 198 pens. As a result, there were an equal number of staplers and pens. How many staplers did she have at first?
| |
Staplers |
Notebooks |
Pens |
| Before |
8 u |
1 u |
|
| Change |
|
- 15 |
|
| After 1 |
|
1 u - 15 |
5 u - 75 |
| Change |
|
|
+ 198 |
| After 2 |
8 u |
1 u - 15 |
5 u + 123 |
Number of notebooks after Victorium gave away 15 notebooks
= 1 u - 15
After Victorium gave away 15 notebooks, the ratio of the number of pens to the number of notebooks became 5 : 1. This means that the number of notebooks was 5 times as many as the number of pens.
Number of pens after Victorium gave away 15 notebooks
= 5 x (1 u - 15)
= 5 u - 75
Number of pens in the end after Victorium bought another 198 pens
= 5 u - 75 + 198
= 5 u + 123
Number of staplers and pens in the end is the same.
8 u = 5 u + 1238 u - 5 u = 1233 u = 123
1 u = 123 ÷ 3 = 41
Total numbers of staplers that Victorium had at first
= 8 u
= 8 x 41
= 328
Answer(s): 328
