Linda and Lynn have some cards. If Linda gives 24 cards to Lynn, Lynn will have 5 times the number of cards as Linda. If Lynn gives 116 cards to Linda, Linda will have
23 as many cards as Lynn. How many cards does Linda have at first?
|
Case 1 |
Case 2 |
|
Linda |
Lynn |
Linda |
Lynn |
Before |
5 u + 24 |
25 u - 24 |
12 u - 116 |
18 u + 116 |
Change |
- 24 |
+ 24 |
+ 116 |
- 116 |
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 Linda had at first is the same in both cases.
12 u - 116 = 5 u + 24
12 u - 5 u = 24 + 116
7 u = 140
1 u = 20
Number of cards that Linda had at first
= 5 u + 24
= 5 x 20 + 24
= 100 + 24
= 124
Answer(s): 124