Roshel and Gabby have some cards. If Roshel gives 17 cards to Gabby, Gabby will have 4 times the number of cards as Roshel. If Gabby gives 123 cards to Roshel, Roshel will have
35 as many cards as Gabby. How many cards does Roshel have at first?
|
Case 1 |
Case 2 |
|
Roshel |
Gabby |
Roshel |
Gabby |
Before |
8 u + 17 |
32 u - 17 |
15 u - 123 |
25 u + 123 |
Change |
- 17 |
+ 17 |
+ 123 |
- 123 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 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 8 is 40.
Number of cards that Roshel had at first is the same in both cases.
15 u - 123 = 8 u + 17
15 u - 8 u = 17 + 123
7 u = 140
1 u = 20
Number of cards that Roshel had at first
= 8 u + 17
= 8 x 20 + 17
= 160 + 17
= 177
Answer(s): 177