Three girls, Fanny, Roshel and Joelle had a total of 5460 buttons. Some exchanges were made. First, Fanny gave Roshel as many buttons as Roshel had. After that, Roshel gave
13 of whatever she had then to Joelle. Finally, Joelle gave
15 of whatever she had to Fanny. As a result, they each had the same number of buttons. How many buttons did Fanny have at first?
|
Fanny |
Roshel |
Joelle |
Total |
Before 1 |
? |
1 u |
|
5460 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5460 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
5460 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5460 |
3 groups = 5460
1 group = 5460 ÷ 3 = 1820
1 group = 4 boxes 4 boxes = 1820
1 box = 1820 ÷ 4 = 455
2 p = 1 group
1 p = 1820 ÷ 2 = 910
3 p = 3 x 910 = 2730
3 p = 2 u
2 u = 2730
1 u = 2730 ÷ 2 = 1365
Number of buttons that Fanny had at first
= 1 group - 1 box + 1 u
= 1820 - 455 + 1365
= 2730
Answer(s): 2730