Wendy had some pencils, staplers and pens. The ratio of the number of pencils to the number of staplers was 7 : 1. After giving away 17 staplers, the ratio of the number of pens to the number of staplers was 5 : 1. Wendy bought another 205 pens. As a result, there were an equal number of pencils and pens. How many staplers did she have at first?
| |
Pencils |
Staplers |
Pens |
| Before |
7 u |
1 u |
|
| Change |
|
- 17 |
|
| After 1 |
|
1 u - 17 |
5 u - 85 |
| Change |
|
|
+ 205 |
| After 2 |
7 u |
1 u - 17 |
5 u + 120 |
Number of staplers after Wendy gave away 17 staplers
= 1 u - 17
After Wendy gave away 17 staplers, the ratio of the number of pens to the number of staplers became 5 : 1. This means that the number of staplers was 5 times as many as the number of pens.
Number of pens after Wendy gave away 17 staplers
= 5 x (1 u - 17)
= 5 u - 85
Number of pens in the end after Wendy bought another 205 pens
= 5 u - 85 + 205
= 5 u + 120
Number of pencils and pens in the end is the same.
7 u = 5 u + 1207 u - 5 u = 1202 u = 120
1 u = 120 ÷ 2 = 60
Total numbers of staplers that Wendy had at first
= 1 u
= 60
Answer(s): 60
