Jade had some pencils, files and markers. The ratio of the number of pencils to the number of files was 6 : 1. After giving away 23 files, the ratio of the number of markers to the number of files was 4 : 1. Jade bought another 190 markers. As a result, there were an equal number of pencils and markers. How many files did she have at first?
| |
Pencils |
Files |
Markers |
| Before |
6 u |
1 u |
|
| Change |
|
- 23 |
|
| After 1 |
|
1 u - 23 |
4 u - 92 |
| Change |
|
|
+ 190 |
| After 2 |
6 u |
1 u - 23 |
4 u + 98 |
Number of files after Jade gave away 23 files
= 1 u - 23
After Jade gave away 23 files, the ratio of the number of markers to the number of files became 4 : 1. This means that the number of files was 4 times as many as the number of markers.
Number of markers after Jade gave away 23 files
= 4 x (1 u - 23)
= 4 u - 92
Number of markers in the end after Jade bought another 190 markers
= 4 u - 92 + 190
= 4 u + 98
Number of pencils and markers in the end is the same.
6 u = 4 u + 986 u - 4 u = 982 u = 98
1 u = 98 ÷ 2 = 49
Total numbers of files that Jade had at first
= 1 u
= 49
Answer(s): 49
