Tiffany had some files, pencils and notebooks. The ratio of the number of files to the number of pencils was 6 : 1. After giving away 24 pencils, the ratio of the number of notebooks to the number of pencils was 3 : 1. Tiffany bought another 171 notebooks. As a result, there were an equal number of files and notebooks. How many pencils did she have at first?
| |
Files |
Pencils |
Notebooks |
| Before |
6 u |
1 u |
|
| Change |
|
- 24 |
|
| After 1 |
|
1 u - 24 |
3 u - 72 |
| Change |
|
|
+ 171 |
| After 2 |
6 u |
1 u - 24 |
3 u + 99 |
Number of pencils after Tiffany gave away 24 pencils
= 1 u - 24
After Tiffany gave away 24 pencils, the ratio of the number of notebooks to the number of pencils became 3 : 1. This means that the number of pencils was 3 times as many as the number of notebooks.
Number of notebooks after Tiffany gave away 24 pencils
= 3 x (1 u - 24)
= 3 u - 72
Number of notebooks in the end after Tiffany bought another 171 notebooks
= 3 u - 72 + 171
= 3 u + 99
Number of files and notebooks in the end is the same.
6 u = 3 u + 996 u - 3 u = 993 u = 99
1 u = 99 ÷ 3 = 33
Total numbers of pencils that Tiffany had at first
= 1 u
= 33
Answer(s): 33
