Esther had some notebooks, markers and files. The ratio of the number of notebooks to the number of markers was 6 : 1. After giving away 30 markers, the ratio of the number of files to the number of markers was 3 : 1. Esther bought another 219 files. As a result, there were an equal number of notebooks and files. How many notebooks did she have at first?
| |
Notebooks |
Markers |
Files |
| Before |
6 u |
1 u |
|
| Change |
|
- 30 |
|
| After 1 |
|
1 u - 30 |
3 u - 90 |
| Change |
|
|
+ 219 |
| After 2 |
6 u |
1 u - 30 |
3 u + 129 |
Number of markers after Esther gave away 30 markers
= 1 u - 30
After Esther gave away 30 markers, the ratio of the number of files to the number of markers became 3 : 1. This means that the number of markers was 3 times as many as the number of files.
Number of files after Esther gave away 30 markers
= 3 x (1 u - 30)
= 3 u - 90
Number of files in the end after Esther bought another 219 files
= 3 u - 90 + 219
= 3 u + 129
Number of notebooks and files in the end is the same.
6 u = 3 u + 1296 u - 3 u = 1293 u = 129
1 u = 129 ÷ 3 = 43
Total numbers of notebooks that Esther had at first
= 6 u
= 6 x 43
= 258
Answer(s): 258
