Three girls, Rachel, Raeann and Cindy had a total of 4590 buttons. Some exchanges were made. First, Rachel gave Raeann as many buttons as Raeann had. After that, Raeann gave
14 of whatever she had then to Cindy. Finally, Cindy gave
14 of whatever she had to Rachel. As a result, they each had the same number of buttons. How many buttons did Rachel have at first?
|
Rachel |
Raeann |
Cindy |
Total |
Before 1 |
? |
1 u |
|
4590 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
4590 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
4 boxes |
4590 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
4590 |
3 groups = 4590
1 group = 4590 ÷ 3 = 1530
1 group = 3 boxes 3 boxes = 1530
1 box = 1530 ÷ 3 = 510
3 p = 1 group
1 p = 1530 ÷ 3 = 510
4 p = 4 x 510 = 2040
4 p = 2 u
2 u = 2040
1 u = 2040 ÷ 2 = 1020
Number of buttons that Rachel had at first
= 1 group - 1 box + 1 u
= 1530 - 510 + 1020
= 2040
Answer(s): 2040