Gabby and Sabrina have some cards. If Gabby gives 12 cards to Sabrina, Sabrina will have 3 times the number of cards as Gabby. If Sabrina gives 6 cards to Gabby, Gabby will have
23 as many cards as Sabrina. How many cards does Gabby have at first?
| |
Case 1 |
Case 2 |
| |
Gabby |
Sabrina |
Gabby |
Sabrina |
| Before |
5 u + 12 |
15 u - 12 |
8 u - 6 |
12 u + 6 |
| Change |
- 12 |
+ 12 |
+ 6 |
- 6 |
| 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 Gabby had at first is the same in both cases.
8 u - 6 = 5 u + 12
8 u - 5 u = 12 + 6
3 u = 18
1 u = 6
Number of cards that Gabby had at first
= 5 u + 12
= 5 x 6 + 12
= 30 + 12
= 42
Answer(s): 42
