Eva had some files, staplers and markers. The ratio of the number of files to the number of staplers was 8 : 1. After giving away 28 staplers, the ratio of the number of markers to the number of staplers was 3 : 1. Eva bought another 174 markers. As a result, there were an equal number of files and markers. How many staplers did she have at first?
| |
Files |
Staplers |
Markers |
| Before |
8 u |
1 u |
|
| Change |
|
- 28 |
|
| After 1 |
|
1 u - 28 |
3 u - 84 |
| Change |
|
|
+ 174 |
| After 2 |
8 u |
1 u - 28 |
3 u + 90 |
Number of staplers after Eva gave away 28 staplers
= 1 u - 28
After Eva gave away 28 staplers, the ratio of the number of markers to the number of staplers became 3 : 1. This means that the number of staplers was 3 times as many as the number of markers.
Number of markers after Eva gave away 28 staplers
= 3 x (1 u - 28)
= 3 u - 84
Number of markers in the end after Eva bought another 174 markers
= 3 u - 84 + 174
= 3 u + 90
Number of files and markers in the end is the same.
8 u = 3 u + 908 u - 3 u = 905 u = 90
1 u = 90 ÷ 5 = 18
Total numbers of staplers that Eva had at first
= 1 u
= 18
Answer(s): 18
