Three girls, Kathy, Yoko and Zara had a total of 1440 beads. Some exchanges were made. First, Kathy gave Yoko as many beads as Yoko had. After that, Yoko gave
13 of whatever she had then to Zara. Finally, Zara gave
14 of whatever she had to Kathy. As a result, they each had the same number of beads. How many beads did Kathy have at first?
|
Kathy |
Yoko |
Zara |
Total |
Before 1 |
? |
1 u |
|
1440 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1440 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
1440 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1440 |
3 groups = 1440
1 group = 1440 ÷ 3 = 480
1 group = 3 boxes 3 boxes = 480
1 box = 480 ÷ 3 = 160
2 p = 1 group
1 p = 480 ÷ 2 = 240
3 p = 3 x 240 = 720
3 p = 2 u
2 u = 720
1 u = 720 ÷ 2 = 360
Number of beads that Kathy had at first
= 1 group - 1 box + 1 u
= 480 - 160 + 360
= 680
Answer(s): 680