Three girls, Nora, Kathy and Cindy had a total of 2250 cards. Some exchanges were made. First, Nora gave Kathy as many cards as Kathy had. After that, Kathy gave
14 of whatever she had then to Cindy. Finally, Cindy gave
14 of whatever she had to Nora. As a result, they each had the same number of cards. How many cards did Nora have at first?
|
Nora |
Kathy |
Cindy |
Total |
Before 1 |
? |
1 u |
|
2250 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
2250 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
4 boxes |
2250 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2250 |
3 groups = 2250
1 group = 2250 ÷ 3 = 750
1 group = 3 boxes 3 boxes = 750
1 box = 750 ÷ 3 = 250
3 p = 1 group
1 p = 750 ÷ 3 = 250
4 p = 4 x 250 = 1000
4 p = 2 u
2 u = 1000
1 u = 1000 ÷ 2 = 500
Number of cards that Nora had at first
= 1 group - 1 box + 1 u
= 750 - 250 + 500
= 1000
Answer(s): 1000