Wendy and Cathy have some cards. If Wendy gives 38 cards to Cathy, Cathy will have 5 times the number of cards as Wendy. If Cathy gives 102 cards to Wendy, Wendy will have
23 as many cards as Cathy. How many cards does Wendy have at first?
|
Case 1 |
Case 2 |
|
Wendy |
Cathy |
Wendy |
Cathy |
Before |
5 u + 38 |
25 u - 38 |
12 u - 102 |
18 u + 102 |
Change |
- 38 |
+ 38 |
+ 102 |
- 102 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 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 5 is 30.
Number of cards that Wendy had at first is the same in both cases.
12 u - 102 = 5 u + 38
12 u - 5 u = 38 + 102
7 u = 140
1 u = 20
Number of cards that Wendy had at first
= 5 u + 38
= 5 x 20 + 38
= 100 + 38
= 138
Answer(s): 138