Marion and Fiona have some cards. If Marion gives 39 cards to Fiona, Fiona will have 5 times the number of cards as Marion. If Fiona gives 80 cards to Marion, Marion will have
23 as many cards as Fiona. How many cards does Marion have at first?
|
Case 1 |
Case 2 |
|
Marion |
Fiona |
Marion |
Fiona |
Before |
5 u + 39 |
25 u - 39 |
12 u - 80 |
18 u + 80 |
Change |
- 39 |
+ 39 |
+ 80 |
- 80 |
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 Marion had at first is the same in both cases.
12 u - 80 = 5 u + 39
12 u - 5 u = 39 + 80
7 u = 119
1 u = 17
Number of cards that Marion had at first
= 5 u + 39
= 5 x 17 + 39
= 85 + 39
= 124
Answer(s): 124