Shiyun had some notebooks, markers and pencils. The ratio of the number of notebooks to the number of markers was 6 : 1. After giving away 26 markers, the ratio of the number of pencils to the number of markers was 4 : 1. Shiyun bought another 186 pencils. As a result, there were an equal number of notebooks and pencils. How many notebooks did she have at first?
| |
Notebooks |
Markers |
Pencils |
| Before |
6 u |
1 u |
|
| Change |
|
- 26 |
|
| After 1 |
|
1 u - 26 |
4 u - 104 |
| Change |
|
|
+ 186 |
| After 2 |
6 u |
1 u - 26 |
4 u + 82 |
Number of markers after Shiyun gave away 26 markers
= 1 u - 26
After Shiyun gave away 26 markers, the ratio of the number of pencils to the number of markers became 4 : 1. This means that the number of markers was 4 times as many as the number of pencils.
Number of pencils after Shiyun gave away 26 markers
= 4 x (1 u - 26)
= 4 u - 104
Number of pencils in the end after Shiyun bought another 186 pencils
= 4 u - 104 + 186
= 4 u + 82
Number of notebooks and pencils in the end is the same.
6 u = 4 u + 826 u - 4 u = 822 u = 82
1 u = 82 ÷ 2 = 41
Total numbers of notebooks that Shiyun had at first
= 6 u
= 6 x 41
= 246
Answer(s): 246
