Gillian and Jaslyn have some cards. If Gillian gives 22 cards to Jaslyn, Jaslyn will have 4 times the number of cards as Gillian. If Jaslyn gives 23 cards to Gillian, Gillian will have
25 as many cards as Jaslyn. How many cards does Gillian have at first?
|
Case 1 |
Case 2 |
|
Gillian |
Jaslyn |
Gillian |
Jaslyn |
Before |
7 u + 22 |
28 u - 22 |
10 u - 23 |
25 u + 23 |
Change |
- 22 |
+ 22 |
+ 23 |
- 23 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
The total number of cards in both cases remains unchanged. Make the total number of cards in both cases the same. LCM of 5 and 7 is 35.
Number of cards that Gillian had at first is the same in both cases.
10 u - 23 = 7 u + 22
10 u - 7 u = 22 + 23
3 u = 45
1 u = 15
Number of cards that Gillian had at first
= 7 u + 22
= 7 x 15 + 22
= 105 + 22
= 127
Answer(s): 127