Sabrina had some pencils, staplers and files. The ratio of the number of pencils to the number of staplers was 6 : 1. After giving away 26 staplers, the ratio of the number of files to the number of staplers was 4 : 1. Sabrina bought another 210 files. As a result, there were an equal number of pencils and files. How many staplers did she have at first?
|
Pencils |
Staplers |
Files |
Before |
6 u |
1 u |
|
Change |
|
- 26 |
|
After 1 |
|
1 u - 26 |
4 u - 104 |
Change |
|
|
+ 210 |
After 2 |
6 u |
1 u - 26 |
4 u + 106 |
Number of staplers after Sabrina gave away 26 staplers
= 1 u - 26
After Sabrina gave away 26 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 Sabrina gave away 26 staplers
= 4 x (1 u - 26)
= 4 u - 104
Number of files in the end after Sabrina bought another 210 files
= 4 u - 104 + 210
= 4 u + 106
Number of pencils and files in the end is the same.
6 u = 4 u + 1066 u - 4 u = 1062 u = 106
1 u = 106 ÷ 2 = 53
Total numbers of staplers that Sabrina had at first
= 1 u
= 53
Answer(s): 53