Xuan had some staplers, pens and markers. The ratio of the number of staplers to the number of pens was 6 : 1. After giving away 18 pens, the ratio of the number of markers to the number of pens was 4 : 1. Xuan bought another 200 markers. As a result, there were an equal number of staplers and markers. How many pens did she have at first?
| |
Staplers |
Pens |
Markers |
| Before |
6 u |
1 u |
|
| Change |
|
- 18 |
|
| After 1 |
|
1 u - 18 |
4 u - 72 |
| Change |
|
|
+ 200 |
| After 2 |
6 u |
1 u - 18 |
4 u + 128 |
Number of pens after Xuan gave away 18 pens
= 1 u - 18
After Xuan gave away 18 pens, the ratio of the number of markers to the number of pens became 4 : 1. This means that the number of pens was 4 times as many as the number of markers.
Number of markers after Xuan gave away 18 pens
= 4 x (1 u - 18)
= 4 u - 72
Number of markers in the end after Xuan bought another 200 markers
= 4 u - 72 + 200
= 4 u + 128
Number of staplers and markers in the end is the same.
6 u = 4 u + 1286 u - 4 u = 1282 u = 128
1 u = 128 ÷ 2 = 64
Total numbers of pens that Xuan had at first
= 1 u
= 64
Answer(s): 64
