Gillian had some pens, staplers and markers. The ratio of the number of pens to the number of staplers was 8 : 1. After giving away 29 staplers, the ratio of the number of markers to the number of staplers was 5 : 1. Gillian bought another 172 markers. As a result, there were an equal number of pens and markers. How many pens did she have at first?
| |
Pens |
Staplers |
Markers |
| Before |
8 u |
1 u |
|
| Change |
|
- 29 |
|
| After 1 |
|
1 u - 29 |
5 u - 145 |
| Change |
|
|
+ 172 |
| After 2 |
8 u |
1 u - 29 |
5 u + 27 |
Number of staplers after Gillian gave away 29 staplers
= 1 u - 29
After Gillian gave away 29 staplers, the ratio of the number of markers to the number of staplers became 5 : 1. This means that the number of staplers was 5 times as many as the number of markers.
Number of markers after Gillian gave away 29 staplers
= 5 x (1 u - 29)
= 5 u - 145
Number of markers in the end after Gillian bought another 172 markers
= 5 u - 145 + 172
= 5 u + 27
Number of pens and markers in the end is the same.
8 u = 5 u + 278 u - 5 u = 273 u = 27
1 u = 27 ÷ 3 = 9
Total numbers of pens that Gillian had at first
= 8 u
= 8 x 9
= 72
Answer(s): 72
