Joelle had some notebooks, files and markers. The ratio of the number of notebooks to the number of files was 8 : 1. After giving away 25 files, the ratio of the number of markers to the number of files was 5 : 1. Joelle bought another 206 markers. As a result, there were an equal number of notebooks and markers. How many files did she have at first?
| |
Notebooks |
Files |
Markers |
| Before |
8 u |
1 u |
|
| Change |
|
- 25 |
|
| After 1 |
|
1 u - 25 |
5 u - 125 |
| Change |
|
|
+ 206 |
| After 2 |
8 u |
1 u - 25 |
5 u + 81 |
Number of files after Joelle gave away 25 files
= 1 u - 25
After Joelle gave away 25 files, the ratio of the number of markers to the number of files became 5 : 1. This means that the number of files was 5 times as many as the number of markers.
Number of markers after Joelle gave away 25 files
= 5 x (1 u - 25)
= 5 u - 125
Number of markers in the end after Joelle bought another 206 markers
= 5 u - 125 + 206
= 5 u + 81
Number of notebooks and markers in the end is the same.
8 u = 5 u + 818 u - 5 u = 813 u = 81
1 u = 81 ÷ 3 = 27
Total numbers of files that Joelle had at first
= 1 u
= 27
Answer(s): 27
