Xuan had some pencils, pens and files. The ratio of the number of pencils to the number of pens was 8 : 1. After giving away 30 pens, the ratio of the number of files to the number of pens was 3 : 1. Xuan bought another 200 files. As a result, there were an equal number of pencils and files. How many pens did she have at first?
| |
Pencils |
Pens |
Files |
| Before |
8 u |
1 u |
|
| Change |
|
- 30 |
|
| After 1 |
|
1 u - 30 |
3 u - 90 |
| Change |
|
|
+ 200 |
| After 2 |
8 u |
1 u - 30 |
3 u + 110 |
Number of pens after Xuan gave away 30 pens
= 1 u - 30
After Xuan gave away 30 pens, the ratio of the number of files to the number of pens became 3 : 1. This means that the number of pens was 3 times as many as the number of files.
Number of files after Xuan gave away 30 pens
= 3 x (1 u - 30)
= 3 u - 90
Number of files in the end after Xuan bought another 200 files
= 3 u - 90 + 200
= 3 u + 110
Number of pencils and files in the end is the same.
8 u = 3 u + 1108 u - 3 u = 1105 u = 110
1 u = 110 ÷ 5 = 22
Total numbers of pens that Xuan had at first
= 1 u
= 22
Answer(s): 22
