Gabby had some files, pens and notebooks. The ratio of the number of files to the number of pens was 6 : 1. After giving away 16 pens, the ratio of the number of notebooks to the number of pens was 3 : 1. Gabby bought another 171 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 |
6 u |
1 u |
|
| Change |
|
- 16 |
|
| After 1 |
|
1 u - 16 |
3 u - 48 |
| Change |
|
|
+ 171 |
| After 2 |
6 u |
1 u - 16 |
3 u + 123 |
Number of pens after Gabby gave away 16 pens
= 1 u - 16
After Gabby gave away 16 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 Gabby gave away 16 pens
= 3 x (1 u - 16)
= 3 u - 48
Number of notebooks in the end after Gabby bought another 171 notebooks
= 3 u - 48 + 171
= 3 u + 123
Number of files and notebooks in the end is the same.
6 u = 3 u + 1236 u - 3 u = 1233 u = 123
1 u = 123 ÷ 3 = 41
Total numbers of pens that Gabby had at first
= 1 u
= 41
Answer(s): 41
