Raeann had some pencils, pens and staplers. The ratio of the number of pencils to the number of pens was 7 : 1. After giving away 21 pens, the ratio of the number of staplers to the number of pens was 5 : 1. Raeann bought another 189 staplers. As a result, there were an equal number of pencils and staplers. How many pens did she have at first?
| |
Pencils |
Pens |
Staplers |
| Before |
7 u |
1 u |
|
| Change |
|
- 21 |
|
| After 1 |
|
1 u - 21 |
5 u - 105 |
| Change |
|
|
+ 189 |
| After 2 |
7 u |
1 u - 21 |
5 u + 84 |
Number of pens after Raeann gave away 21 pens
= 1 u - 21
After Raeann gave away 21 pens, the ratio of the number of staplers to the number of pens became 5 : 1. This means that the number of pens was 5 times as many as the number of staplers.
Number of staplers after Raeann gave away 21 pens
= 5 x (1 u - 21)
= 5 u - 105
Number of staplers in the end after Raeann bought another 189 staplers
= 5 u - 105 + 189
= 5 u + 84
Number of pencils and staplers in the end is the same.
7 u = 5 u + 847 u - 5 u = 842 u = 84
1 u = 84 ÷ 2 = 42
Total numbers of pens that Raeann had at first
= 1 u
= 42
Answer(s): 42
