Nicole had some pencils, staplers and files. The ratio of the number of pencils to the number of staplers was 8 : 1. After giving away 24 staplers, the ratio of the number of files to the number of staplers was 4 : 1. Nicole bought another 152 files. As a result, there were an equal number of pencils and files. How many pencils did she have at first?
| |
Pencils |
Staplers |
Files |
| Before |
8 u |
1 u |
|
| Change |
|
- 24 |
|
| After 1 |
|
1 u - 24 |
4 u - 96 |
| Change |
|
|
+ 152 |
| After 2 |
8 u |
1 u - 24 |
4 u + 56 |
Number of staplers after Nicole gave away 24 staplers
= 1 u - 24
After Nicole gave away 24 staplers, the ratio of the number of files to the number of staplers became 4 : 1. This means that the number of staplers was 4 times as many as the number of files.
Number of files after Nicole gave away 24 staplers
= 4 x (1 u - 24)
= 4 u - 96
Number of files in the end after Nicole bought another 152 files
= 4 u - 96 + 152
= 4 u + 56
Number of pencils and files in the end is the same.
8 u = 4 u + 568 u - 4 u = 564 u = 56
1 u = 56 ÷ 4 = 14
Total numbers of pencils that Nicole had at first
= 8 u
= 8 x 14
= 112
Answer(s): 112
