Anna and Raeann have some cards. If Anna gives 18 cards to Raeann, Raeann will have 5 times the number of cards as Anna. If Raeann gives 67 cards to Anna, Anna will have
35 as many cards as Raeann. How many cards does Anna have at first?
|
Case 1 |
Case 2 |
|
Anna |
Raeann |
Anna |
Raeann |
Before |
4 u + 18 |
20 u - 18 |
9 u - 67 |
15 u + 67 |
Change |
- 18 |
+ 18 |
+ 67 |
- 67 |
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 Anna had at first is the same in both cases.
9 u - 67 = 4 u + 18
9 u - 4 u = 18 + 67
5 u = 85
1 u = 17
Number of cards that Anna had at first
= 4 u + 18
= 4 x 17 + 18
= 68 + 18
= 86
Answer(s): 86