Joelle had some pencils, pens and files. The ratio of the number of pencils to the number of pens was 6 : 1. After giving away 18 pens, the ratio of the number of files to the number of pens was 3 : 1. Joelle bought another 174 files. As a result, there were an equal number of pencils and files. How many pencils did she have at first?
| |
Pencils |
Pens |
Files |
| Before |
6 u |
1 u |
|
| Change |
|
- 18 |
|
| After 1 |
|
1 u - 18 |
3 u - 54 |
| Change |
|
|
+ 174 |
| After 2 |
6 u |
1 u - 18 |
3 u + 120 |
Number of pens after Joelle gave away 18 pens
= 1 u - 18
After Joelle gave away 18 pens, the ratio of the number of files to the number of pens became 3 : 1. This means that the number of pens was 3 times as many as the number of files.
Number of files after Joelle gave away 18 pens
= 3 x (1 u - 18)
= 3 u - 54
Number of files in the end after Joelle bought another 174 files
= 3 u - 54 + 174
= 3 u + 120
Number of pencils and files in the end is the same.
6 u = 3 u + 1206 u - 3 u = 1203 u = 120
1 u = 120 ÷ 3 = 40
Total numbers of pencils that Joelle had at first
= 6 u
= 6 x 40
= 240
Answer(s): 240
