Gem had some pencils, staplers and markers. The ratio of the number of pencils to the number of staplers was 6 : 1. After giving away 28 staplers, the ratio of the number of markers to the number of staplers was 4 : 1. Gem bought another 174 markers. As a result, there were an equal number of pencils and markers. How many staplers did she have at first?
|
Pencils |
Staplers |
Markers |
Before |
6 u |
1 u |
|
Change |
|
- 28 |
|
After 1 |
|
1 u - 28 |
4 u - 112 |
Change |
|
|
+ 174 |
After 2 |
6 u |
1 u - 28 |
4 u + 62 |
Number of staplers after Gem gave away 28 staplers
= 1 u - 28
After Gem gave away 28 staplers, the ratio of the number of markers to the number of staplers became 4 : 1. This means that the number of staplers was 4 times as many as the number of markers.
Number of markers after Gem gave away 28 staplers
= 4 x (1 u - 28)
= 4 u - 112
Number of markers in the end after Gem bought another 174 markers
= 4 u - 112 + 174
= 4 u + 62
Number of pencils and markers in the end is the same.
6 u = 4 u + 626 u - 4 u = 622 u = 62
1 u = 62 ÷ 2 = 31
Total numbers of staplers that Gem had at first
= 1 u
= 31
Answer(s): 31