Marion had some files, pens and staplers. The ratio of the number of files to the number of pens was 8 : 1. After giving away 26 pens, the ratio of the number of staplers to the number of pens was 5 : 1. Marion bought another 178 staplers. As a result, there were an equal number of files and staplers. How many files did she have at first?
| |
Files |
Pens |
Staplers |
| Before |
8 u |
1 u |
|
| Change |
|
- 26 |
|
| After 1 |
|
1 u - 26 |
5 u - 130 |
| Change |
|
|
+ 178 |
| After 2 |
8 u |
1 u - 26 |
5 u + 48 |
Number of pens after Marion gave away 26 pens
= 1 u - 26
After Marion gave away 26 pens, the ratio of the number of staplers to the number of pens became 5 : 1. This means that the number of pens was 5 times as many as the number of staplers.
Number of staplers after Marion gave away 26 pens
= 5 x (1 u - 26)
= 5 u - 130
Number of staplers in the end after Marion bought another 178 staplers
= 5 u - 130 + 178
= 5 u + 48
Number of files and staplers in the end is the same.
8 u = 5 u + 488 u - 5 u = 483 u = 48
1 u = 48 ÷ 3 = 16
Total numbers of files that Marion had at first
= 8 u
= 8 x 16
= 128
Answer(s): 128
