Emily had some files, notebooks and pencils. The ratio of the number of files to the number of notebooks was 7 : 1. After giving away 24 notebooks, the ratio of the number of pencils to the number of notebooks was 4 : 1. Emily bought another 150 pencils. As a result, there were an equal number of files and pencils. How many files did she have at first?
| |
Files |
Notebooks |
Pencils |
| Before |
7 u |
1 u |
|
| Change |
|
- 24 |
|
| After 1 |
|
1 u - 24 |
4 u - 96 |
| Change |
|
|
+ 150 |
| After 2 |
7 u |
1 u - 24 |
4 u + 54 |
Number of notebooks after Emily gave away 24 notebooks
= 1 u - 24
After Emily gave away 24 notebooks, the ratio of the number of pencils to the number of notebooks became 4 : 1. This means that the number of notebooks was 4 times as many as the number of pencils.
Number of pencils after Emily gave away 24 notebooks
= 4 x (1 u - 24)
= 4 u - 96
Number of pencils in the end after Emily bought another 150 pencils
= 4 u - 96 + 150
= 4 u + 54
Number of files and pencils in the end is the same.
7 u = 4 u + 547 u - 4 u = 543 u = 54
1 u = 54 ÷ 3 = 18
Total numbers of files that Emily had at first
= 7 u
= 7 x 18
= 126
Answer(s): 126
