Raeann had some pens, notebooks and pencils. The ratio of the number of pens to the number of notebooks was 6 : 1. After giving away 30 notebooks, the ratio of the number of pencils to the number of notebooks was 4 : 1. Raeann bought another 216 pencils. As a result, there were an equal number of pens and pencils. How many pens did she have at first?
| |
Pens |
Notebooks |
Pencils |
| Before |
6 u |
1 u |
|
| Change |
|
- 30 |
|
| After 1 |
|
1 u - 30 |
4 u - 120 |
| Change |
|
|
+ 216 |
| After 2 |
6 u |
1 u - 30 |
4 u + 96 |
Number of notebooks after Raeann gave away 30 notebooks
= 1 u - 30
After Raeann gave away 30 notebooks, the ratio of the number of pencils to the number of notebooks became 4 : 1. This means that the number of notebooks was 4 times as many as the number of pencils.
Number of pencils after Raeann gave away 30 notebooks
= 4 x (1 u - 30)
= 4 u - 120
Number of pencils in the end after Raeann bought another 216 pencils
= 4 u - 120 + 216
= 4 u + 96
Number of pens and pencils in the end is the same.
6 u = 4 u + 966 u - 4 u = 962 u = 96
1 u = 96 ÷ 2 = 48
Total numbers of pens that Raeann had at first
= 6 u
= 6 x 48
= 288
Answer(s): 288
