Xuan had some staplers, pens and notebooks. The ratio of the number of staplers to the number of pens was 6 : 1. After giving away 16 pens, the ratio of the number of notebooks to the number of pens was 4 : 1. Xuan bought another 170 notebooks. As a result, there were an equal number of staplers and notebooks. How many staplers did she have at first?
| |
Staplers |
Pens |
Notebooks |
| Before |
6 u |
1 u |
|
| Change |
|
- 16 |
|
| After 1 |
|
1 u - 16 |
4 u - 64 |
| Change |
|
|
+ 170 |
| After 2 |
6 u |
1 u - 16 |
4 u + 106 |
Number of pens after Xuan gave away 16 pens
= 1 u - 16
After Xuan gave away 16 pens, the ratio of the number of notebooks to the number of pens became 4 : 1. This means that the number of pens was 4 times as many as the number of notebooks.
Number of notebooks after Xuan gave away 16 pens
= 4 x (1 u - 16)
= 4 u - 64
Number of notebooks in the end after Xuan bought another 170 notebooks
= 4 u - 64 + 170
= 4 u + 106
Number of staplers and notebooks in the end is the same.
6 u = 4 u + 1066 u - 4 u = 1062 u = 106
1 u = 106 ÷ 2 = 53
Total numbers of staplers that Xuan had at first
= 6 u
= 6 x 53
= 318
Answer(s): 318
