Jane and Yen have some cards. If Jane gives 24 cards to Yen, Yen will have 5 times the number of cards as Jane. If Yen gives 11 cards to Jane, Jane will have
35 as many cards as Yen. How many cards does Jane have at first?
|
Case 1 |
Case 2 |
|
Jane |
Yen |
Jane |
Yen |
Before |
4 u + 24 |
20 u - 24 |
9 u - 11 |
15 u + 11 |
Change |
- 24 |
+ 24 |
+ 11 |
- 11 |
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 - 11 = 4 u + 24
9 u - 4 u = 24 + 11
5 u = 35
1 u = 7
Number of cards that Jane had at first
= 4 u + 24
= 4 x 7 + 24
= 28 + 24
= 52
Answer(s): 52