Xandra had some notebooks, pens and files. The ratio of the number of notebooks to the number of pens was 7 : 1. After giving away 17 pens, the ratio of the number of files to the number of pens was 4 : 1. Xandra bought another 173 files. As a result, there were an equal number of notebooks and files. How many notebooks did she have at first?
| |
Notebooks |
Pens |
Files |
| Before |
7 u |
1 u |
|
| Change |
|
- 17 |
|
| After 1 |
|
1 u - 17 |
4 u - 68 |
| Change |
|
|
+ 173 |
| After 2 |
7 u |
1 u - 17 |
4 u + 105 |
Number of pens after Xandra gave away 17 pens
= 1 u - 17
After Xandra gave away 17 pens, the ratio of the number of files to the number of pens became 4 : 1. This means that the number of pens was 4 times as many as the number of files.
Number of files after Xandra gave away 17 pens
= 4 x (1 u - 17)
= 4 u - 68
Number of files in the end after Xandra bought another 173 files
= 4 u - 68 + 173
= 4 u + 105
Number of notebooks and files in the end is the same.
7 u = 4 u + 1057 u - 4 u = 1053 u = 105
1 u = 105 ÷ 3 = 35
Total numbers of notebooks that Xandra had at first
= 7 u
= 7 x 35
= 245
Answer(s): 245
