Gabby had some pencils, files and notebooks. The ratio of the number of pencils to the number of files was 7 : 1. After giving away 27 files, the ratio of the number of notebooks to the number of files was 3 : 1. Gabby bought another 161 notebooks. As a result, there were an equal number of pencils and notebooks. How many pencils did she have at first?
| |
Pencils |
Files |
Notebooks |
| Before |
7 u |
1 u |
|
| Change |
|
- 27 |
|
| After 1 |
|
1 u - 27 |
3 u - 81 |
| Change |
|
|
+ 161 |
| After 2 |
7 u |
1 u - 27 |
3 u + 80 |
Number of files after Gabby gave away 27 files
= 1 u - 27
After Gabby gave away 27 files, the ratio of the number of notebooks to the number of files became 3 : 1. This means that the number of files was 3 times as many as the number of notebooks.
Number of notebooks after Gabby gave away 27 files
= 3 x (1 u - 27)
= 3 u - 81
Number of notebooks in the end after Gabby bought another 161 notebooks
= 3 u - 81 + 161
= 3 u + 80
Number of pencils and notebooks in the end is the same.
7 u = 3 u + 807 u - 3 u = 804 u = 80
1 u = 80 ÷ 4 = 20
Total numbers of pencils that Gabby had at first
= 7 u
= 7 x 20
= 140
Answer(s): 140
