Three girls, Jean, Julie and Joelle had a total of 3780 cards. Some exchanges were made. First, Jean gave Julie as many cards as Julie had. After that, Julie gave
13 of whatever she had then to Joelle. Finally, Joelle gave
13 of whatever she had to Jean. As a result, they each had the same number of cards. How many cards did Jean have at first?
|
Jean |
Julie |
Joelle |
Total |
Before 1 |
? |
1 u |
|
3780 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
3780 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
3780 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
3780 |
3 groups = 3780
1 group = 3780 ÷ 3 = 1260
1 group = 2 boxes 2 boxes = 1260
1 box = 1260 ÷ 2 = 630
2 p = 1 group
1 p = 1260 ÷ 2 = 630
3 p = 3 x 630 = 1890
3 p = 2 u
2 u = 1890
1 u = 1890 ÷ 2 = 945
Number of cards that Jean had at first
= 1 group - 1 box + 1 u
= 1260 - 630 + 945
= 1575
Answer(s): 1575