Three girls, Yen, Roshel and Kylie had a total of 4500 cards. Some exchanges were made. First, Yen gave Roshel as many cards as Roshel had. After that, Roshel gave
13 of whatever she had then to Kylie. Finally, Kylie gave
15 of whatever she had to Yen. As a result, they each had the same number of cards. How many cards did Yen have at first?
|
Yen |
Roshel |
Kylie |
Total |
Before 1 |
? |
1 u |
|
4500 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
4500 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
4500 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
4500 |
3 groups = 4500
1 group = 4500 ÷ 3 = 1500
1 group = 4 boxes 4 boxes = 1500
1 box = 1500 ÷ 4 = 375
2 p = 1 group
1 p = 1500 ÷ 2 = 750
3 p = 3 x 750 = 2250
3 p = 2 u
2 u = 2250
1 u = 2250 ÷ 2 = 1125
Number of cards that Yen had at first
= 1 group - 1 box + 1 u
= 1500 - 375 + 1125
= 2250
Answer(s): 2250