Gillian had some files, pens and notebooks. The ratio of the number of files to the number of pens was 8 : 1. After giving away 28 pens, the ratio of the number of notebooks to the number of pens was 5 : 1. Gillian bought another 158 notebooks. As a result, there were an equal number of files and notebooks. How many pens did she have at first?
| |
Files |
Pens |
Notebooks |
| Before |
8 u |
1 u |
|
| Change |
|
- 28 |
|
| After 1 |
|
1 u - 28 |
5 u - 140 |
| Change |
|
|
+ 158 |
| After 2 |
8 u |
1 u - 28 |
5 u + 18 |
Number of pens after Gillian gave away 28 pens
= 1 u - 28
After Gillian gave away 28 pens, the ratio of the number of notebooks to the number of pens became 5 : 1. This means that the number of pens was 5 times as many as the number of notebooks.
Number of notebooks after Gillian gave away 28 pens
= 5 x (1 u - 28)
= 5 u - 140
Number of notebooks in the end after Gillian bought another 158 notebooks
= 5 u - 140 + 158
= 5 u + 18
Number of files and notebooks in the end is the same.
8 u = 5 u + 188 u - 5 u = 183 u = 18
1 u = 18 ÷ 3 = 6
Total numbers of pens that Gillian had at first
= 1 u
= 6
Answer(s): 6
