Xylia and Usha have some cards. If Xylia gives 36 cards to Usha, Usha will have 5 times the number of cards as Xylia. If Usha gives 24 cards to Xylia, Xylia will have
25 as many cards as Usha. How many cards does Xylia have at first?
|
Case 1 |
Case 2 |
|
Xylia |
Usha |
Xylia |
Usha |
Before |
7 u + 36 |
35 u - 36 |
12 u - 24 |
30 u + 24 |
Change |
- 36 |
+ 36 |
+ 24 |
- 24 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of cards that Xylia had at first is the same in both cases.
12 u - 24 = 7 u + 36
12 u - 7 u = 36 + 24
5 u = 60
1 u = 12
Number of cards that Xylia had at first
= 7 u + 36
= 7 x 12 + 36
= 84 + 36
= 120
Answer(s): 120