Three girls, Shiyun, Usha and Xylia had a total of 4020 beads. Some exchanges were made. First, Shiyun gave Usha as many beads as Usha had. After that, Usha gave
13 of whatever she had then to Xylia. Finally, Xylia gave
13 of whatever she had to Shiyun. As a result, they each had the same number of beads. How many beads did Shiyun have at first?
|
Shiyun |
Usha |
Xylia |
Total |
Before 1 |
? |
1 u |
|
4020 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
4020 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
4020 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
4020 |
3 groups = 4020
1 group = 4020 ÷ 3 = 1340
1 group = 2 boxes 2 boxes = 1340
1 box = 1340 ÷ 2 = 670
2 p = 1 group
1 p = 1340 ÷ 2 = 670
3 p = 3 x 670 = 2010
3 p = 2 u
2 u = 2010
1 u = 2010 ÷ 2 = 1005
Number of beads that Shiyun had at first
= 1 group - 1 box + 1 u
= 1340 - 670 + 1005
= 1675
Answer(s): 1675