Kylie and Opal have some cards. If Kylie gives 22 cards to Opal, Opal will have 5 times the number of cards as Kylie. If Opal gives 8 cards to Kylie, Kylie will have
25 as many cards as Opal. How many cards does Kylie have at first?
|
Case 1 |
Case 2 |
|
Kylie |
Opal |
Kylie |
Opal |
Before |
7 u + 22 |
35 u - 22 |
12 u - 8 |
30 u + 8 |
Change |
- 22 |
+ 22 |
+ 8 |
- 8 |
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 Kylie had at first is the same in both cases.
12 u - 8 = 7 u + 22
12 u - 7 u = 22 + 8
5 u = 30
1 u = 6
Number of cards that Kylie had at first
= 7 u + 22
= 7 x 6 + 22
= 42 + 22
= 64
Answer(s): 64