Tiffany had some files, markers and staplers. The ratio of the number of files to the number of markers was 6 : 1. After giving away 16 markers, the ratio of the number of staplers to the number of markers was 3 : 1. Tiffany bought another 177 staplers. As a result, there were an equal number of files and staplers. How many files did she have at first?
| |
Files |
Markers |
Staplers |
| Before |
6 u |
1 u |
|
| Change |
|
- 16 |
|
| After 1 |
|
1 u - 16 |
3 u - 48 |
| Change |
|
|
+ 177 |
| After 2 |
6 u |
1 u - 16 |
3 u + 129 |
Number of markers after Tiffany gave away 16 markers
= 1 u - 16
After Tiffany gave away 16 markers, the ratio of the number of staplers to the number of markers became 3 : 1. This means that the number of markers was 3 times as many as the number of staplers.
Number of staplers after Tiffany gave away 16 markers
= 3 x (1 u - 16)
= 3 u - 48
Number of staplers in the end after Tiffany bought another 177 staplers
= 3 u - 48 + 177
= 3 u + 129
Number of files and staplers in the end is the same.
6 u = 3 u + 1296 u - 3 u = 1293 u = 129
1 u = 129 ÷ 3 = 43
Total numbers of files that Tiffany had at first
= 6 u
= 6 x 43
= 258
Answer(s): 258
