Three girls, Yen, Lynn and Lucy had a total of 810 cards. Some exchanges were made. First, Yen gave Lynn as many cards as Lynn had. After that, Lynn gave
14 of whatever she had then to Lucy. Finally, Lucy gave
14 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 |
Lynn |
Lucy |
Total |
Before 1 |
? |
1 u |
|
810 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
810 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
4 boxes |
810 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
810 |
3 groups = 810
1 group = 810 ÷ 3 = 270
1 group = 3 boxes 3 boxes = 270
1 box = 270 ÷ 3 = 90
3 p = 1 group
1 p = 270 ÷ 3 = 90
4 p = 4 x 90 = 360
4 p = 2 u
2 u = 360
1 u = 360 ÷ 2 = 180
Number of cards that Yen had at first
= 1 group - 1 box + 1 u
= 270 - 90 + 180
= 360
Answer(s): 360