Barbara had some files, notebooks and pens. The ratio of the number of files to the number of notebooks was 8 : 1. After giving away 17 notebooks, the ratio of the number of pens to the number of notebooks was 5 : 1. Barbara bought another 208 pens. As a result, there were an equal number of files and pens. How many notebooks did she have at first?
| |
Files |
Notebooks |
Pens |
| Before |
8 u |
1 u |
|
| Change |
|
- 17 |
|
| After 1 |
|
1 u - 17 |
5 u - 85 |
| Change |
|
|
+ 208 |
| After 2 |
8 u |
1 u - 17 |
5 u + 123 |
Number of notebooks after Barbara gave away 17 notebooks
= 1 u - 17
After Barbara gave away 17 notebooks, the ratio of the number of pens to the number of notebooks became 5 : 1. This means that the number of notebooks was 5 times as many as the number of pens.
Number of pens after Barbara gave away 17 notebooks
= 5 x (1 u - 17)
= 5 u - 85
Number of pens in the end after Barbara bought another 208 pens
= 5 u - 85 + 208
= 5 u + 123
Number of files and pens in the end is the same.
8 u = 5 u + 1238 u - 5 u = 1233 u = 123
1 u = 123 ÷ 3 = 41
Total numbers of notebooks that Barbara had at first
= 1 u
= 41
Answer(s): 41
