Fiona had some notebooks, files and pens. The ratio of the number of notebooks to the number of files was 8 : 1. After giving away 27 files, the ratio of the number of pens to the number of files was 5 : 1. Fiona bought another 150 pens. As a result, there were an equal number of notebooks and pens. How many notebooks did she have at first?
| |
Notebooks |
Files |
Pens |
| Before |
8 u |
1 u |
|
| Change |
|
- 27 |
|
| After 1 |
|
1 u - 27 |
5 u - 135 |
| Change |
|
|
+ 150 |
| After 2 |
8 u |
1 u - 27 |
5 u + 15 |
Number of files after Fiona gave away 27 files
= 1 u - 27
After Fiona gave away 27 files, the ratio of the number of pens to the number of files became 5 : 1. This means that the number of files was 5 times as many as the number of pens.
Number of pens after Fiona gave away 27 files
= 5 x (1 u - 27)
= 5 u - 135
Number of pens in the end after Fiona bought another 150 pens
= 5 u - 135 + 150
= 5 u + 15
Number of notebooks and pens in the end is the same.
8 u = 5 u + 158 u - 5 u = 153 u = 15
1 u = 15 ÷ 3 = 5
Total numbers of notebooks that Fiona had at first
= 8 u
= 8 x 5
= 40
Answer(s): 40
