Three girls, Lucy, Julie and Diana had a total of 2040 cards. Some exchanges were made. First, Lucy gave Julie as many cards as Julie had. After that, Julie gave
15 of whatever she had then to Diana. Finally, Diana gave
15 of whatever she had to Lucy. As a result, they each had the same number of cards. How many cards did Lucy have at first?
|
Lucy |
Julie |
Diana |
Total |
Before 1 |
? |
1 u |
|
2040 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
2040 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
5 boxes |
2040 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2040 |
3 groups = 2040
1 group = 2040 ÷ 3 = 680
1 group = 4 boxes 4 boxes = 680
1 box = 680 ÷ 4 = 170
4 p = 1 group
1 p = 680 ÷ 4 = 170
5 p = 5 x 170 = 850
5 p = 2 u
2 u = 850
1 u = 850 ÷ 2 = 425
Number of cards that Lucy had at first
= 1 group - 1 box + 1 u
= 680 - 170 + 425
= 935
Answer(s): 935