Erika had some pencils, markers and staplers. The ratio of the number of pencils to the number of markers was 6 : 1. After giving away 30 markers, the ratio of the number of staplers to the number of markers was 4 : 1. Erika bought another 168 staplers. As a result, there were an equal number of pencils and staplers. How many markers did she have at first?
| |
Pencils |
Markers |
Staplers |
| Before |
6 u |
1 u |
|
| Change |
|
- 30 |
|
| After 1 |
|
1 u - 30 |
4 u - 120 |
| Change |
|
|
+ 168 |
| After 2 |
6 u |
1 u - 30 |
4 u + 48 |
Number of markers after Erika gave away 30 markers
= 1 u - 30
After Erika gave away 30 markers, the ratio of the number of staplers to the number of markers became 4 : 1. This means that the number of markers was 4 times as many as the number of staplers.
Number of staplers after Erika gave away 30 markers
= 4 x (1 u - 30)
= 4 u - 120
Number of staplers in the end after Erika bought another 168 staplers
= 4 u - 120 + 168
= 4 u + 48
Number of pencils and staplers in the end is the same.
6 u = 4 u + 486 u - 4 u = 482 u = 48
1 u = 48 ÷ 2 = 24
Total numbers of markers that Erika had at first
= 1 u
= 24
Answer(s): 24
