Penelope had some pencils, markers and notebooks. The ratio of the number of pencils to the number of markers was 8 : 1. After giving away 15 markers, the ratio of the number of notebooks to the number of markers was 4 : 1. Penelope bought another 184 notebooks. As a result, there were an equal number of pencils and notebooks. How many pencils did she have at first?
| |
Pencils |
Markers |
Notebooks |
| Before |
8 u |
1 u |
|
| Change |
|
- 15 |
|
| After 1 |
|
1 u - 15 |
4 u - 60 |
| Change |
|
|
+ 184 |
| After 2 |
8 u |
1 u - 15 |
4 u + 124 |
Number of markers after Penelope gave away 15 markers
= 1 u - 15
After Penelope gave away 15 markers, the ratio of the number of notebooks to the number of markers became 4 : 1. This means that the number of markers was 4 times as many as the number of notebooks.
Number of notebooks after Penelope gave away 15 markers
= 4 x (1 u - 15)
= 4 u - 60
Number of notebooks in the end after Penelope bought another 184 notebooks
= 4 u - 60 + 184
= 4 u + 124
Number of pencils and notebooks in the end is the same.
8 u = 4 u + 1248 u - 4 u = 1244 u = 124
1 u = 124 ÷ 4 = 31
Total numbers of pencils that Penelope had at first
= 8 u
= 8 x 31
= 248
Answer(s): 248
