Nora had some notebooks, markers and files. The ratio of the number of notebooks to the number of markers was 8 : 1. After giving away 24 markers, the ratio of the number of files to the number of markers was 5 : 1. Nora bought another 168 files. As a result, there were an equal number of notebooks and files. How many markers did she have at first?
| |
Notebooks |
Markers |
Files |
| Before |
8 u |
1 u |
|
| Change |
|
- 24 |
|
| After 1 |
|
1 u - 24 |
5 u - 120 |
| Change |
|
|
+ 168 |
| After 2 |
8 u |
1 u - 24 |
5 u + 48 |
Number of markers after Nora gave away 24 markers
= 1 u - 24
After Nora gave away 24 markers, the ratio of the number of files to the number of markers became 5 : 1. This means that the number of markers was 5 times as many as the number of files.
Number of files after Nora gave away 24 markers
= 5 x (1 u - 24)
= 5 u - 120
Number of files in the end after Nora bought another 168 files
= 5 u - 120 + 168
= 5 u + 48
Number of notebooks and files in the end is the same.
8 u = 5 u + 488 u - 5 u = 483 u = 48
1 u = 48 ÷ 3 = 16
Total numbers of markers that Nora had at first
= 1 u
= 16
Answer(s): 16
