Three girls, Penelope, Julie and Usha had a total of 1680 buttons. Some exchanges were made. First, Penelope gave Julie as many buttons as Julie had. After that, Julie gave
15 of whatever she had then to Usha. Finally, Usha gave
15 of whatever she had to Penelope. As a result, they each had the same number of buttons. How many buttons did Penelope have at first?
|
Penelope |
Julie |
Usha |
Total |
Before 1 |
? |
1 u |
|
1680 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
1680 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
5 boxes |
1680 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1680 |
3 groups = 1680
1 group = 1680 ÷ 3 = 560
1 group = 4 boxes 4 boxes = 560
1 box = 560 ÷ 4 = 140
4 p = 1 group
1 p = 560 ÷ 4 = 140
5 p = 5 x 140 = 700
5 p = 2 u
2 u = 700
1 u = 700 ÷ 2 = 350
Number of buttons that Penelope had at first
= 1 group - 1 box + 1 u
= 560 - 140 + 350
= 770
Answer(s): 770