Gem had some notebooks, staplers and pens. The ratio of the number of notebooks to the number of staplers was 8 : 1. After giving away 24 staplers, the ratio of the number of pens to the number of staplers was 5 : 1. Gem bought another 210 pens. As a result, there were an equal number of notebooks and pens. How many staplers did she have at first?
| |
Notebooks |
Staplers |
Pens |
| Before |
8 u |
1 u |
|
| Change |
|
- 24 |
|
| After 1 |
|
1 u - 24 |
5 u - 120 |
| Change |
|
|
+ 210 |
| After 2 |
8 u |
1 u - 24 |
5 u + 90 |
Number of staplers after Gem gave away 24 staplers
= 1 u - 24
After Gem gave away 24 staplers, the ratio of the number of pens to the number of staplers became 5 : 1. This means that the number of staplers was 5 times as many as the number of pens.
Number of pens after Gem gave away 24 staplers
= 5 x (1 u - 24)
= 5 u - 120
Number of pens in the end after Gem bought another 210 pens
= 5 u - 120 + 210
= 5 u + 90
Number of notebooks and pens in the end is the same.
8 u = 5 u + 908 u - 5 u = 903 u = 90
1 u = 90 ÷ 3 = 30
Total numbers of staplers that Gem had at first
= 1 u
= 30
Answer(s): 30
