Penelope had some pens, files and markers. The ratio of the number of pens to the number of files was 7 : 1. After giving away 28 files, the ratio of the number of markers to the number of files was 4 : 1. Penelope bought another 178 markers. As a result, there were an equal number of pens and markers. How many pens did she have at first?
| |
Pens |
Files |
Markers |
| Before |
7 u |
1 u |
|
| Change |
|
- 28 |
|
| After 1 |
|
1 u - 28 |
4 u - 112 |
| Change |
|
|
+ 178 |
| After 2 |
7 u |
1 u - 28 |
4 u + 66 |
Number of files after Penelope gave away 28 files
= 1 u - 28
After Penelope gave away 28 files, the ratio of the number of markers to the number of files became 4 : 1. This means that the number of files was 4 times as many as the number of markers.
Number of markers after Penelope gave away 28 files
= 4 x (1 u - 28)
= 4 u - 112
Number of markers in the end after Penelope bought another 178 markers
= 4 u - 112 + 178
= 4 u + 66
Number of pens and markers in the end is the same.
7 u = 4 u + 667 u - 4 u = 663 u = 66
1 u = 66 ÷ 3 = 22
Total numbers of pens that Penelope had at first
= 7 u
= 7 x 22
= 154
Answer(s): 154
