Min had some pens, markers and pencils. The ratio of the number of pens to the number of markers was 6 : 1. After giving away 30 markers, the ratio of the number of pencils to the number of markers was 3 : 1. Min bought another 174 pencils. As a result, there were an equal number of pens and pencils. How many pens did she have at first?
|
Pens |
Markers |
Pencils |
Before |
6 u |
1 u |
|
Change |
|
- 30 |
|
After 1 |
|
1 u - 30 |
3 u - 90 |
Change |
|
|
+ 174 |
After 2 |
6 u |
1 u - 30 |
3 u + 84 |
Number of markers after Min gave away 30 markers
= 1 u - 30
After Min gave away 30 markers, the ratio of the number of pencils to the number of markers became 3 : 1. This means that the number of markers was 3 times as many as the number of pencils.
Number of pencils after Min gave away 30 markers
= 3 x (1 u - 30)
= 3 u - 90
Number of pencils in the end after Min bought another 174 pencils
= 3 u - 90 + 174
= 3 u + 84
Number of pens and pencils in the end is the same.
6 u = 3 u + 846 u - 3 u = 843 u = 84
1 u = 84 ÷ 3 = 28
Total numbers of pens that Min had at first
= 6 u
= 6 x 28
= 168
Answer(s): 168