Kathy had some notebooks, markers and staplers. The ratio of the number of notebooks to the number of markers was 6 : 1. After giving away 24 markers, the ratio of the number of staplers to the number of markers was 3 : 1. Kathy bought another 213 staplers. As a result, there were an equal number of notebooks and staplers. How many markers did she have at first?
| |
Notebooks |
Markers |
Staplers |
| Before |
6 u |
1 u |
|
| Change |
|
- 24 |
|
| After 1 |
|
1 u - 24 |
3 u - 72 |
| Change |
|
|
+ 213 |
| After 2 |
6 u |
1 u - 24 |
3 u + 141 |
Number of markers after Kathy gave away 24 markers
= 1 u - 24
After Kathy gave away 24 markers, the ratio of the number of staplers to the number of markers became 3 : 1. This means that the number of markers was 3 times as many as the number of staplers.
Number of staplers after Kathy gave away 24 markers
= 3 x (1 u - 24)
= 3 u - 72
Number of staplers in the end after Kathy bought another 213 staplers
= 3 u - 72 + 213
= 3 u + 141
Number of notebooks and staplers in the end is the same.
6 u = 3 u + 1416 u - 3 u = 1413 u = 141
1 u = 141 ÷ 3 = 47
Total numbers of markers that Kathy had at first
= 1 u
= 47
Answer(s): 47
