Three girls, Gwen, Gillian and Marion had a total of 2880 buttons. Some exchanges were made. First, Gwen gave Gillian as many buttons as Gillian had. After that, Gillian gave
15 of whatever she had then to Marion. Finally, Marion gave
13 of whatever she had to Gwen. As a result, they each had the same number of buttons. How many buttons did Gwen have at first?
|
Gwen |
Gillian |
Marion |
Total |
Before 1 |
? |
1 u |
|
2880 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
2880 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
3 boxes |
2880 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2880 |
3 groups = 2880
1 group = 2880 ÷ 3 = 960
1 group = 2 boxes 2 boxes = 960
1 box = 960 ÷ 2 = 480
4 p = 1 group
1 p = 960 ÷ 4 = 240
5 p = 5 x 240 = 1200
5 p = 2 u
2 u = 1200
1 u = 1200 ÷ 2 = 600
Number of buttons that Gwen had at first
= 1 group - 1 box + 1 u
= 960 - 480 + 600
= 1080
Answer(s): 1080