Three girls, Xylia, Opal and Cindy had a total of 5400 erasers. Some exchanges were made. First, Xylia gave Opal as many erasers as Opal had. After that, Opal gave
14 of whatever she had then to Cindy. Finally, Cindy gave
14 of whatever she had to Xylia. As a result, they each had the same number of erasers. How many erasers did Xylia have at first?
|
Xylia |
Opal |
Cindy |
Total |
Before 1 |
? |
1 u |
|
5400 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
5400 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
4 boxes |
5400 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5400 |
3 groups = 5400
1 group = 5400 ÷ 3 = 1800
1 group = 3 boxes 3 boxes = 1800
1 box = 1800 ÷ 3 = 600
3 p = 1 group
1 p = 1800 ÷ 3 = 600
4 p = 4 x 600 = 2400
4 p = 2 u
2 u = 2400
1 u = 2400 ÷ 2 = 1200
Number of erasers that Xylia had at first
= 1 group - 1 box + 1 u
= 1800 - 600 + 1200
= 2400
Answer(s): 2400