Yen had some notebooks, markers and pencils. The ratio of the number of notebooks to the number of markers was 6 : 1. After giving away 20 markers, the ratio of the number of pencils to the number of markers was 3 : 1. Yen bought another 153 pencils. As a result, there were an equal number of notebooks and pencils. How many markers did she have at first?
| |
Notebooks |
Markers |
Pencils |
| Before |
6 u |
1 u |
|
| Change |
|
- 20 |
|
| After 1 |
|
1 u - 20 |
3 u - 60 |
| Change |
|
|
+ 153 |
| After 2 |
6 u |
1 u - 20 |
3 u + 93 |
Number of markers after Yen gave away 20 markers
= 1 u - 20
After Yen gave away 20 markers, the ratio of the number of pencils to the number of markers became 3 : 1. This means that the number of markers was 3 times as many as the number of pencils.
Number of pencils after Yen gave away 20 markers
= 3 x (1 u - 20)
= 3 u - 60
Number of pencils in the end after Yen bought another 153 pencils
= 3 u - 60 + 153
= 3 u + 93
Number of notebooks and pencils in the end is the same.
6 u = 3 u + 936 u - 3 u = 933 u = 93
1 u = 93 ÷ 3 = 31
Total numbers of markers that Yen had at first
= 1 u
= 31
Answer(s): 31
