Three girls, Yen, Xylia and Shiyun had a total of 3960 erasers. Some exchanges were made. First, Yen gave Xylia as many erasers as Xylia had. After that, Xylia gave
14 of whatever she had then to Shiyun. Finally, Shiyun gave
13 of whatever she had to Yen. As a result, they each had the same number of erasers. How many erasers did Yen have at first?
|
Yen |
Xylia |
Shiyun |
Total |
Before 1 |
? |
1 u |
|
3960 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
3960 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
3 boxes |
3960 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
3960 |
3 groups = 3960
1 group = 3960 ÷ 3 = 1320
1 group = 2 boxes 2 boxes = 1320
1 box = 1320 ÷ 2 = 660
3 p = 1 group
1 p = 1320 ÷ 3 = 440
4 p = 4 x 440 = 1760
4 p = 2 u
2 u = 1760
1 u = 1760 ÷ 2 = 880
Number of erasers that Yen had at first
= 1 group - 1 box + 1 u
= 1320 - 660 + 880
= 1540
Answer(s): 1540