Tiffany had some pencils, notebooks and markers. The ratio of the number of pencils to the number of notebooks was 6 : 1. After giving away 29 notebooks, the ratio of the number of markers to the number of notebooks was 3 : 1. Tiffany bought another 189 markers. As a result, there were an equal number of pencils and markers. How many pencils did she have at first?
| |
Pencils |
Notebooks |
Markers |
| Before |
6 u |
1 u |
|
| Change |
|
- 29 |
|
| After 1 |
|
1 u - 29 |
3 u - 87 |
| Change |
|
|
+ 189 |
| After 2 |
6 u |
1 u - 29 |
3 u + 102 |
Number of notebooks after Tiffany gave away 29 notebooks
= 1 u - 29
After Tiffany gave away 29 notebooks, the ratio of the number of markers to the number of notebooks became 3 : 1. This means that the number of notebooks was 3 times as many as the number of markers.
Number of markers after Tiffany gave away 29 notebooks
= 3 x (1 u - 29)
= 3 u - 87
Number of markers in the end after Tiffany bought another 189 markers
= 3 u - 87 + 189
= 3 u + 102
Number of pencils and markers in the end is the same.
6 u = 3 u + 1026 u - 3 u = 1023 u = 102
1 u = 102 ÷ 3 = 34
Total numbers of pencils that Tiffany had at first
= 6 u
= 6 x 34
= 204
Answer(s): 204
