Tiffany and Shannon have some cards. If Tiffany gives 39 cards to Shannon, Shannon will have 5 times the number of cards as Tiffany. If Shannon gives 31 cards to Tiffany, Tiffany will have
25 as many cards as Shannon. How many cards does Tiffany have at first?
|
Case 1 |
Case 2 |
|
Tiffany |
Shannon |
Tiffany |
Shannon |
Before |
7 u + 39 |
35 u - 39 |
12 u - 31 |
30 u + 31 |
Change |
- 39 |
+ 39 |
+ 31 |
- 31 |
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 Tiffany had at first is the same in both cases.
12 u - 31 = 7 u + 39
12 u - 7 u = 39 + 31
5 u = 70
1 u = 14
Number of cards that Tiffany had at first
= 7 u + 39
= 7 x 14 + 39
= 98 + 39
= 137
Answer(s): 137