Julie had some files, notebooks and pencils. The ratio of the number of files to the number of notebooks was 7 : 1. After giving away 18 notebooks, the ratio of the number of pencils to the number of notebooks was 3 : 1. Julie bought another 210 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 |
|
- 18 |
|
| After 1 |
|
1 u - 18 |
3 u - 54 |
| Change |
|
|
+ 210 |
| After 2 |
7 u |
1 u - 18 |
3 u + 156 |
Number of notebooks after Julie gave away 18 notebooks
= 1 u - 18
After Julie gave away 18 notebooks, the ratio of the number of pencils to the number of notebooks became 3 : 1. This means that the number of notebooks was 3 times as many as the number of pencils.
Number of pencils after Julie gave away 18 notebooks
= 3 x (1 u - 18)
= 3 u - 54
Number of pencils in the end after Julie bought another 210 pencils
= 3 u - 54 + 210
= 3 u + 156
Number of files and pencils in the end is the same.
7 u = 3 u + 1567 u - 3 u = 1564 u = 156
1 u = 156 ÷ 4 = 39
Total numbers of files that Julie had at first
= 7 u
= 7 x 39
= 273
Answer(s): 273
