Three girls, Barbara, Lucy and Natalie had a total of 5160 buttons. Some exchanges were made. First, Barbara gave Lucy as many buttons as Lucy had. After that, Lucy gave
15 of whatever she had then to Natalie. Finally, Natalie gave
15 of whatever she had to Barbara. As a result, they each had the same number of buttons. How many buttons did Barbara have at first?
|
Barbara |
Lucy |
Natalie |
Total |
Before 1 |
? |
1 u |
|
5160 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
5160 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
5 boxes |
5160 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5160 |
3 groups = 5160
1 group = 5160 ÷ 3 = 1720
1 group = 4 boxes 4 boxes = 1720
1 box = 1720 ÷ 4 = 430
4 p = 1 group
1 p = 1720 ÷ 4 = 430
5 p = 5 x 430 = 2150
5 p = 2 u
2 u = 2150
1 u = 2150 ÷ 2 = 1075
Number of buttons that Barbara had at first
= 1 group - 1 box + 1 u
= 1720 - 430 + 1075
= 2365
Answer(s): 2365