Risa had some pencils, pens and markers. The ratio of the number of pencils to the number of pens was 7 : 1. After giving away 28 pens, the ratio of the number of markers to the number of pens was 4 : 1. Risa bought another 193 markers. As a result, there were an equal number of pencils and markers. How many pencils did she have at first?
| |
Pencils |
Pens |
Markers |
| Before |
7 u |
1 u |
|
| Change |
|
- 28 |
|
| After 1 |
|
1 u - 28 |
4 u - 112 |
| Change |
|
|
+ 193 |
| After 2 |
7 u |
1 u - 28 |
4 u + 81 |
Number of pens after Risa gave away 28 pens
= 1 u - 28
After Risa gave away 28 pens, the ratio of the number of markers to the number of pens became 4 : 1. This means that the number of pens was 4 times as many as the number of markers.
Number of markers after Risa gave away 28 pens
= 4 x (1 u - 28)
= 4 u - 112
Number of markers in the end after Risa bought another 193 markers
= 4 u - 112 + 193
= 4 u + 81
Number of pencils and markers in the end is the same.
7 u = 4 u + 817 u - 4 u = 813 u = 81
1 u = 81 ÷ 3 = 27
Total numbers of pencils that Risa had at first
= 7 u
= 7 x 27
= 189
Answer(s): 189
