Zoe had some markers, notebooks and files. The ratio of the number of markers to the number of notebooks was 7 : 1. After giving away 23 notebooks, the ratio of the number of files to the number of notebooks was 4 : 1. Zoe bought another 173 files. As a result, there were an equal number of markers and files. How many notebooks did she have at first?
| |
Markers |
Notebooks |
Files |
| Before |
7 u |
1 u |
|
| Change |
|
- 23 |
|
| After 1 |
|
1 u - 23 |
4 u - 92 |
| Change |
|
|
+ 173 |
| After 2 |
7 u |
1 u - 23 |
4 u + 81 |
Number of notebooks after Zoe gave away 23 notebooks
= 1 u - 23
After Zoe gave away 23 notebooks, the ratio of the number of files to the number of notebooks became 4 : 1. This means that the number of notebooks was 4 times as many as the number of files.
Number of files after Zoe gave away 23 notebooks
= 4 x (1 u - 23)
= 4 u - 92
Number of files in the end after Zoe bought another 173 files
= 4 u - 92 + 173
= 4 u + 81
Number of markers and files in the end is the same.
7 u = 4 u + 817 u - 4 u = 813 u = 81
1 u = 81 ÷ 3 = 27
Total numbers of notebooks that Zoe had at first
= 1 u
= 27
Answer(s): 27
