Olivium had some notebooks, staplers and pens. The ratio of the number of notebooks to the number of staplers was 6 : 1. After giving away 23 staplers, the ratio of the number of pens to the number of staplers was 4 : 1. Olivium bought another 202 pens. As a result, there were an equal number of notebooks and pens. How many notebooks did she have at first?
| |
Notebooks |
Staplers |
Pens |
| Before |
6 u |
1 u |
|
| Change |
|
- 23 |
|
| After 1 |
|
1 u - 23 |
4 u - 92 |
| Change |
|
|
+ 202 |
| After 2 |
6 u |
1 u - 23 |
4 u + 110 |
Number of staplers after Olivium gave away 23 staplers
= 1 u - 23
After Olivium gave away 23 staplers, the ratio of the number of pens to the number of staplers became 4 : 1. This means that the number of staplers was 4 times as many as the number of pens.
Number of pens after Olivium gave away 23 staplers
= 4 x (1 u - 23)
= 4 u - 92
Number of pens in the end after Olivium bought another 202 pens
= 4 u - 92 + 202
= 4 u + 110
Number of notebooks and pens in the end is the same.
6 u = 4 u + 1106 u - 4 u = 1102 u = 110
1 u = 110 ÷ 2 = 55
Total numbers of notebooks that Olivium had at first
= 6 u
= 6 x 55
= 330
Answer(s): 330
