Three girls, Rachel, Opal and Winnie had a total of 3000 buttons. Some exchanges were made. First, Rachel gave Opal as many buttons as Opal had. After that, Opal gave
13 of whatever she had then to Winnie. Finally, Winnie gave
15 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 |
Opal |
Winnie |
Total |
Before 1 |
? |
1 u |
|
3000 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
3000 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
3000 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
3000 |
3 groups = 3000
1 group = 3000 ÷ 3 = 1000
1 group = 4 boxes 4 boxes = 1000
1 box = 1000 ÷ 4 = 250
2 p = 1 group
1 p = 1000 ÷ 2 = 500
3 p = 3 x 500 = 1500
3 p = 2 u
2 u = 1500
1 u = 1500 ÷ 2 = 750
Number of buttons that Rachel had at first
= 1 group - 1 box + 1 u
= 1000 - 250 + 750
= 1500
Answer(s): 1500