Wendy had some staplers, files and pens. The ratio of the number of staplers to the number of files was 7 : 1. After giving away 25 files, the ratio of the number of pens to the number of files was 5 : 1. Wendy bought another 201 pens. As a result, there were an equal number of staplers and pens. How many files did she have at first?
| |
Staplers |
Files |
Pens |
| Before |
7 u |
1 u |
|
| Change |
|
- 25 |
|
| After 1 |
|
1 u - 25 |
5 u - 125 |
| Change |
|
|
+ 201 |
| After 2 |
7 u |
1 u - 25 |
5 u + 76 |
Number of files after Wendy gave away 25 files
= 1 u - 25
After Wendy gave away 25 files, the ratio of the number of pens to the number of files became 5 : 1. This means that the number of files was 5 times as many as the number of pens.
Number of pens after Wendy gave away 25 files
= 5 x (1 u - 25)
= 5 u - 125
Number of pens in the end after Wendy bought another 201 pens
= 5 u - 125 + 201
= 5 u + 76
Number of staplers and pens in the end is the same.
7 u = 5 u + 767 u - 5 u = 762 u = 76
1 u = 76 ÷ 2 = 38
Total numbers of files that Wendy had at first
= 1 u
= 38
Answer(s): 38
