Wendy had some staplers, notebooks and pens. The ratio of the number of staplers to the number of notebooks was 6 : 1. After giving away 16 notebooks, the ratio of the number of pens to the number of notebooks was 3 : 1. Wendy bought another 219 pens. As a result, there were an equal number of staplers and pens. How many notebooks did she have at first?
| |
Staplers |
Notebooks |
Pens |
| Before |
6 u |
1 u |
|
| Change |
|
- 16 |
|
| After 1 |
|
1 u - 16 |
3 u - 48 |
| Change |
|
|
+ 219 |
| After 2 |
6 u |
1 u - 16 |
3 u + 171 |
Number of notebooks after Wendy gave away 16 notebooks
= 1 u - 16
After Wendy gave away 16 notebooks, the ratio of the number of pens to the number of notebooks became 3 : 1. This means that the number of notebooks was 3 times as many as the number of pens.
Number of pens after Wendy gave away 16 notebooks
= 3 x (1 u - 16)
= 3 u - 48
Number of pens in the end after Wendy bought another 219 pens
= 3 u - 48 + 219
= 3 u + 171
Number of staplers and pens in the end is the same.
6 u = 3 u + 1716 u - 3 u = 1713 u = 171
1 u = 171 ÷ 3 = 57
Total numbers of notebooks that Wendy had at first
= 1 u
= 57
Answer(s): 57
