Tina had some notebooks, pens and staplers. The ratio of the number of notebooks to the number of pens was 8 : 1. After giving away 18 pens, the ratio of the number of staplers to the number of pens was 5 : 1. Tina bought another 171 staplers. As a result, there were an equal number of notebooks and staplers. How many pens did she have at first?
| |
Notebooks |
Pens |
Staplers |
| Before |
8 u |
1 u |
|
| Change |
|
- 18 |
|
| After 1 |
|
1 u - 18 |
5 u - 90 |
| Change |
|
|
+ 171 |
| After 2 |
8 u |
1 u - 18 |
5 u + 81 |
Number of pens after Tina gave away 18 pens
= 1 u - 18
After Tina gave away 18 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 Tina gave away 18 pens
= 5 x (1 u - 18)
= 5 u - 90
Number of staplers in the end after Tina bought another 171 staplers
= 5 u - 90 + 171
= 5 u + 81
Number of notebooks and staplers in the end is the same.
8 u = 5 u + 818 u - 5 u = 813 u = 81
1 u = 81 ÷ 3 = 27
Total numbers of pens that Tina had at first
= 1 u
= 27
Answer(s): 27
