Olivium had some staplers, pencils and pens. The ratio of the number of staplers to the number of pencils was 6 : 1. After giving away 21 pencils, the ratio of the number of pens to the number of pencils was 3 : 1. Olivium bought another 210 pens. As a result, there were an equal number of staplers and pens. How many staplers did she have at first?
| |
Staplers |
Pencils |
Pens |
| Before |
6 u |
1 u |
|
| Change |
|
- 21 |
|
| After 1 |
|
1 u - 21 |
3 u - 63 |
| Change |
|
|
+ 210 |
| After 2 |
6 u |
1 u - 21 |
3 u + 147 |
Number of pencils after Olivium gave away 21 pencils
= 1 u - 21
After Olivium gave away 21 pencils, the ratio of the number of pens to the number of pencils became 3 : 1. This means that the number of pencils was 3 times as many as the number of pens.
Number of pens after Olivium gave away 21 pencils
= 3 x (1 u - 21)
= 3 u - 63
Number of pens in the end after Olivium bought another 210 pens
= 3 u - 63 + 210
= 3 u + 147
Number of staplers and pens in the end is the same.
6 u = 3 u + 1476 u - 3 u = 1473 u = 147
1 u = 147 ÷ 3 = 49
Total numbers of staplers that Olivium had at first
= 6 u
= 6 x 49
= 294
Answer(s): 294
