Risa and Nora have some cards. If Risa gives 19 cards to Nora, Nora will have 4 times the number of cards as Risa. If Nora gives 29 cards to Risa, Risa will have
25 as many cards as Nora. How many cards does Risa have at first?
|
Case 1 |
Case 2 |
|
Risa |
Nora |
Risa |
Nora |
Before |
7 u + 19 |
28 u - 19 |
10 u - 29 |
25 u + 29 |
Change |
- 19 |
+ 19 |
+ 29 |
- 29 |
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 Risa had at first is the same in both cases.
10 u - 29 = 7 u + 19
10 u - 7 u = 19 + 29
3 u = 48
1 u = 16
Number of cards that Risa had at first
= 7 u + 19
= 7 x 16 + 19
= 112 + 19
= 131
Answer(s): 131