Yoko and Opal have some cards. If Yoko gives 36 cards to Opal, Opal will have 5 times the number of cards as Yoko. If Opal gives 54 cards to Yoko, Yoko will have
35 as many cards as Opal. How many cards does Yoko have at first?
|
Case 1 |
Case 2 |
|
Yoko |
Opal |
Yoko |
Opal |
Before |
4 u + 36 |
20 u - 36 |
9 u - 54 |
15 u + 54 |
Change |
- 36 |
+ 36 |
+ 54 |
- 54 |
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 Yoko had at first is the same in both cases.
9 u - 54 = 4 u + 36
9 u - 4 u = 36 + 54
5 u = 90
1 u = 18
Number of cards that Yoko had at first
= 4 u + 36
= 4 x 18 + 36
= 72 + 36
= 108
Answer(s): 108