Xylia and Erika have some cards. If Xylia gives 22 cards to Erika, Erika will have 3 times the number of cards as Xylia. If Erika gives 5 cards to Xylia, Xylia will have
23 as many cards as Erika. How many cards does Xylia have at first?
|
Case 1 |
Case 2 |
|
Xylia |
Erika |
Xylia |
Erika |
Before |
5 u + 22 |
15 u - 22 |
8 u - 5 |
12 u + 5 |
Change |
- 22 |
+ 22 |
+ 5 |
- 5 |
After |
1x5 = 5 u |
3x5 = 15 u |
2x4 = 8 u |
3x4 = 12 u |
The total number of cards in both cases remains unchanged. Make the total number of cards in both cases the same. LCM of 4 and 5 is 20.
Number of cards that Xylia had at first is the same in both cases.
8 u - 5 = 5 u + 22
8 u - 5 u = 22 + 5
3 u = 27
1 u = 9
Number of cards that Xylia had at first
= 5 u + 22
= 5 x 9 + 22
= 45 + 22
= 67
Answer(s): 67