Gem had some pencils, pens and notebooks. The ratio of the number of pencils to the number of pens was 7 : 1. After giving away 28 pens, the ratio of the number of notebooks to the number of pens was 3 : 1. Gem bought another 192 notebooks. As a result, there were an equal number of pencils and notebooks. How many pens did she have at first?
| |
Pencils |
Pens |
Notebooks |
| Before |
7 u |
1 u |
|
| Change |
|
- 28 |
|
| After 1 |
|
1 u - 28 |
3 u - 84 |
| Change |
|
|
+ 192 |
| After 2 |
7 u |
1 u - 28 |
3 u + 108 |
Number of pens after Gem gave away 28 pens
= 1 u - 28
After Gem gave away 28 pens, the ratio of the number of notebooks to the number of pens became 3 : 1. This means that the number of pens was 3 times as many as the number of notebooks.
Number of notebooks after Gem gave away 28 pens
= 3 x (1 u - 28)
= 3 u - 84
Number of notebooks in the end after Gem bought another 192 notebooks
= 3 u - 84 + 192
= 3 u + 108
Number of pencils and notebooks in the end is the same.
7 u = 3 u + 1087 u - 3 u = 1084 u = 108
1 u = 108 ÷ 4 = 27
Total numbers of pens that Gem had at first
= 1 u
= 27
Answer(s): 27
