Wendy had some staplers, files and markers. The ratio of the number of staplers to the number of files was 6 : 1. After giving away 22 files, the ratio of the number of markers to the number of files was 3 : 1. Wendy bought another 216 markers. As a result, there were an equal number of staplers and markers. How many files did she have at first?
| |
Staplers |
Files |
Markers |
| Before |
6 u |
1 u |
|
| Change |
|
- 22 |
|
| After 1 |
|
1 u - 22 |
3 u - 66 |
| Change |
|
|
+ 216 |
| After 2 |
6 u |
1 u - 22 |
3 u + 150 |
Number of files after Wendy gave away 22 files
= 1 u - 22
After Wendy gave away 22 files, the ratio of the number of markers to the number of files became 3 : 1. This means that the number of files was 3 times as many as the number of markers.
Number of markers after Wendy gave away 22 files
= 3 x (1 u - 22)
= 3 u - 66
Number of markers in the end after Wendy bought another 216 markers
= 3 u - 66 + 216
= 3 u + 150
Number of staplers and markers in the end is the same.
6 u = 3 u + 1506 u - 3 u = 1503 u = 150
1 u = 150 ÷ 3 = 50
Total numbers of files that Wendy had at first
= 1 u
= 50
Answer(s): 50
