Gem and Min have some cards. If Gem gives 29 cards to Min, Min will have 5 times the number of cards as Gem. If Min gives 51 cards to Gem, Gem will have
35 as many cards as Min. How many cards does Gem have at first?
|
Case 1 |
Case 2 |
|
Gem |
Min |
Gem |
Min |
Before |
4 u + 29 |
20 u - 29 |
9 u - 51 |
15 u + 51 |
Change |
- 29 |
+ 29 |
+ 51 |
- 51 |
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 Gem had at first is the same in both cases.
9 u - 51 = 4 u + 29
9 u - 4 u = 29 + 51
5 u = 80
1 u = 16
Number of cards that Gem had at first
= 4 u + 29
= 4 x 16 + 29
= 64 + 29
= 93
Answer(s): 93