Marion and Yen have some cards. If Marion gives 17 cards to Yen, Yen will have 5 times the number of cards as Marion. If Yen gives 33 cards to Marion, Marion will have
35 as many cards as Yen. How many cards does Marion have at first?
|
Case 1 |
Case 2 |
|
Marion |
Yen |
Marion |
Yen |
Before |
4 u + 17 |
20 u - 17 |
9 u - 33 |
15 u + 33 |
Change |
- 17 |
+ 17 |
+ 33 |
- 33 |
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 Marion had at first is the same in both cases.
9 u - 33 = 4 u + 17
9 u - 4 u = 17 + 33
5 u = 50
1 u = 10
Number of cards that Marion had at first
= 4 u + 17
= 4 x 10 + 17
= 40 + 17
= 57
Answer(s): 57