Three girls, Winnie, Yoko and Betty had a total of 5580 buttons. Some exchanges were made. First, Winnie gave Yoko as many buttons as Yoko had. After that, Yoko gave
13 of whatever she had then to Betty. Finally, Betty gave
14 of whatever she had to Winnie. As a result, they each had the same number of buttons. How many buttons did Winnie have at first?
|
Winnie |
Yoko |
Betty |
Total |
Before 1 |
? |
1 u |
|
5580 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5580 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
5580 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5580 |
3 groups = 5580
1 group = 5580 ÷ 3 = 1860
1 group = 3 boxes 3 boxes = 1860
1 box = 1860 ÷ 3 = 620
2 p = 1 group
1 p = 1860 ÷ 2 = 930
3 p = 3 x 930 = 2790
3 p = 2 u
2 u = 2790
1 u = 2790 ÷ 2 = 1395
Number of buttons that Winnie had at first
= 1 group - 1 box + 1 u
= 1860 - 620 + 1395
= 2635
Answer(s): 2635