Jane and Shiyun have some cards. If Jane gives 13 cards to Shiyun, Shiyun will have 5 times the number of cards as Jane. If Shiyun gives 37 cards to Jane, Jane will have
35 as many cards as Shiyun. How many cards does Jane have at first?
| |
Case 1 |
Case 2 |
| |
Jane |
Shiyun |
Jane |
Shiyun |
| Before |
4 u + 13 |
20 u - 13 |
9 u - 37 |
15 u + 37 |
| Change |
- 13 |
+ 13 |
+ 37 |
- 37 |
| After |
1x4 =
4 u |
5x4 =
20 u |
3x3 =
9 u |
5x3 =
15 u |
The total number of cards in both cases remains unchanged. Make the total number of cards in both cases the same. LCM of 6 and 8 is 24.
Number of cards that Jane had at first is the same in both cases.
9 u - 37 = 4 u + 13
9 u - 4 u = 13 + 37
5 u = 50
1 u = 10
Number of cards that Jane had at first
= 4 u + 13
= 4 x 10 + 13
= 40 + 13
= 53
Answer(s): 53
