Raeann had some pencils, markers and notebooks. The ratio of the number of pencils to the number of markers was 6 : 1. After giving away 22 markers, the ratio of the number of notebooks to the number of markers was 4 : 1. Raeann bought another 150 notebooks. As a result, there were an equal number of pencils and notebooks. How many markers did she have at first?
| |
Pencils |
Markers |
Notebooks |
| Before |
6 u |
1 u |
|
| Change |
|
- 22 |
|
| After 1 |
|
1 u - 22 |
4 u - 88 |
| Change |
|
|
+ 150 |
| After 2 |
6 u |
1 u - 22 |
4 u + 62 |
Number of markers after Raeann gave away 22 markers
= 1 u - 22
After Raeann gave away 22 markers, the ratio of the number of notebooks to the number of markers became 4 : 1. This means that the number of markers was 4 times as many as the number of notebooks.
Number of notebooks after Raeann gave away 22 markers
= 4 x (1 u - 22)
= 4 u - 88
Number of notebooks in the end after Raeann bought another 150 notebooks
= 4 u - 88 + 150
= 4 u + 62
Number of pencils and notebooks in the end is the same.
6 u = 4 u + 626 u - 4 u = 622 u = 62
1 u = 62 ÷ 2 = 31
Total numbers of markers that Raeann had at first
= 1 u
= 31
Answer(s): 31
