Three girls, Kylie, Yen and Tammy had a total of 810 buttons. Some exchanges were made. First, Kylie gave Yen as many buttons as Yen had. After that, Yen gave
14 of whatever she had then to Tammy. Finally, Tammy gave
13 of whatever she had to Kylie. As a result, they each had the same number of buttons. How many buttons did Kylie have at first?
|
Kylie |
Yen |
Tammy |
Total |
Before 1 |
? |
1 u |
|
810 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
810 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
3 boxes |
810 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
810 |
3 groups = 810
1 group = 810 ÷ 3 = 270
1 group = 2 boxes 2 boxes = 270
1 box = 270 ÷ 2 = 135
3 p = 1 group
1 p = 270 ÷ 3 = 90
4 p = 4 x 90 = 360
4 p = 2 u
2 u = 360
1 u = 360 ÷ 2 = 180
Number of buttons that Kylie had at first
= 1 group - 1 box + 1 u
= 270 - 135 + 180
= 315
Answer(s): 315