Three girls, Winnie, Natalie and Fiona had a total of 360 buttons. Some exchanges were made. First, Winnie gave Natalie as many buttons as Natalie had. After that, Natalie gave
15 of whatever she had then to Fiona. Finally, Fiona gave
13 of whatever she had to Winnie. As a result, they each had the same number of buttons. How many buttons did Winnie have at first?
|
Winnie |
Natalie |
Fiona |
Total |
Before 1 |
? |
1 u |
|
360 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
360 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
3 boxes |
360 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
360 |
3 groups = 360
1 group = 360 ÷ 3 = 120
1 group = 2 boxes 2 boxes = 120
1 box = 120 ÷ 2 = 60
4 p = 1 group
1 p = 120 ÷ 4 = 30
5 p = 5 x 30 = 150
5 p = 2 u
2 u = 150
1 u = 150 ÷ 2 = 75
Number of buttons that Winnie had at first
= 1 group - 1 box + 1 u
= 120 - 60 + 75
= 135
Answer(s): 135