Eva had some markers, pencils and notebooks. The ratio of the number of markers to the number of pencils was 7 : 1. After giving away 21 pencils, the ratio of the number of notebooks to the number of pencils was 5 : 1. Eva bought another 207 notebooks. As a result, there were an equal number of markers and notebooks. How many markers did she have at first?
| |
Markers |
Pencils |
Notebooks |
| Before |
7 u |
1 u |
|
| Change |
|
- 21 |
|
| After 1 |
|
1 u - 21 |
5 u - 105 |
| Change |
|
|
+ 207 |
| After 2 |
7 u |
1 u - 21 |
5 u + 102 |
Number of pencils after Eva gave away 21 pencils
= 1 u - 21
After Eva gave away 21 pencils, the ratio of the number of notebooks to the number of pencils became 5 : 1. This means that the number of pencils was 5 times as many as the number of notebooks.
Number of notebooks after Eva gave away 21 pencils
= 5 x (1 u - 21)
= 5 u - 105
Number of notebooks in the end after Eva bought another 207 notebooks
= 5 u - 105 + 207
= 5 u + 102
Number of markers and notebooks in the end is the same.
7 u = 5 u + 1027 u - 5 u = 1022 u = 102
1 u = 102 ÷ 2 = 51
Total numbers of markers that Eva had at first
= 7 u
= 7 x 51
= 357
Answer(s): 357
