Gem had some notebooks, pencils and files. The ratio of the number of notebooks to the number of pencils was 6 : 1. After giving away 18 pencils, the ratio of the number of files to the number of pencils was 3 : 1. Gem bought another 201 files. As a result, there were an equal number of notebooks and files. How many notebooks did she have at first?
| |
Notebooks |
Pencils |
Files |
| Before |
6 u |
1 u |
|
| Change |
|
- 18 |
|
| After 1 |
|
1 u - 18 |
3 u - 54 |
| Change |
|
|
+ 201 |
| After 2 |
6 u |
1 u - 18 |
3 u + 147 |
Number of pencils after Gem gave away 18 pencils
= 1 u - 18
After Gem gave away 18 pencils, the ratio of the number of files to the number of pencils became 3 : 1. This means that the number of pencils was 3 times as many as the number of files.
Number of files after Gem gave away 18 pencils
= 3 x (1 u - 18)
= 3 u - 54
Number of files in the end after Gem bought another 201 files
= 3 u - 54 + 201
= 3 u + 147
Number of notebooks and files in the end is the same.
6 u = 3 u + 1476 u - 3 u = 1473 u = 147
1 u = 147 ÷ 3 = 49
Total numbers of notebooks that Gem had at first
= 6 u
= 6 x 49
= 294
Answer(s): 294
