Three girls, Xylia, Victoria and Zara had a total of 3420 buttons. Some exchanges were made. First, Xylia gave Victoria as many buttons as Victoria had. After that, Victoria gave
13 of whatever she had then to Zara. Finally, Zara gave
15 of whatever she had to Xylia. As a result, they each had the same number of buttons. How many buttons did Xylia have at first?
|
Xylia |
Victoria |
Zara |
Total |
Before 1 |
? |
1 u |
|
3420 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
3420 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
3420 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
3420 |
3 groups = 3420
1 group = 3420 ÷ 3 = 1140
1 group = 4 boxes 4 boxes = 1140
1 box = 1140 ÷ 4 = 285
2 p = 1 group
1 p = 1140 ÷ 2 = 570
3 p = 3 x 570 = 1710
3 p = 2 u
2 u = 1710
1 u = 1710 ÷ 2 = 855
Number of buttons that Xylia had at first
= 1 group - 1 box + 1 u
= 1140 - 285 + 855
= 1710
Answer(s): 1710