Three girls, Natalie, Risa and Kathy had a total of 3060 cards. Some exchanges were made. First, Natalie gave Risa as many cards as Risa had. After that, Risa gave
14 of whatever she had then to Kathy. Finally, Kathy gave
15 of whatever she had to Natalie. As a result, they each had the same number of cards. How many cards did Natalie have at first?
|
Natalie |
Risa |
Kathy |
Total |
Before 1 |
? |
1 u |
|
3060 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
3060 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
5 boxes |
3060 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
3060 |
3 groups = 3060
1 group = 3060 ÷ 3 = 1020
1 group = 4 boxes 4 boxes = 1020
1 box = 1020 ÷ 4 = 255
3 p = 1 group
1 p = 1020 ÷ 3 = 340
4 p = 4 x 340 = 1360
4 p = 2 u
2 u = 1360
1 u = 1360 ÷ 2 = 680
Number of cards that Natalie had at first
= 1 group - 1 box + 1 u
= 1020 - 255 + 680
= 1445
Answer(s): 1445