Three girls, Penelope, Julie and Wendy had a total of 1440 pens. Some exchanges were made. First, Penelope gave Julie as many pens as Julie had. After that, Julie gave
13 of whatever she had then to Wendy. Finally, Wendy gave
14 of whatever she had to Penelope. As a result, they each had the same number of pens. How many pens did Penelope have at first?
|
Penelope |
Julie |
Wendy |
Total |
Before 1 |
? |
1 u |
|
1440 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1440 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
1440 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1440 |
3 groups = 1440
1 group = 1440 ÷ 3 = 480
1 group = 3 boxes 3 boxes = 480
1 box = 480 ÷ 3 = 160
2 p = 1 group
1 p = 480 ÷ 2 = 240
3 p = 3 x 240 = 720
3 p = 2 u
2 u = 720
1 u = 720 ÷ 2 = 360
Number of pens that Penelope had at first
= 1 group - 1 box + 1 u
= 480 - 160 + 360
= 680
Answer(s): 680