Esther and Hilda have some cards. If Esther gives 24 cards to Hilda, Hilda will have 5 times the number of cards as Esther. If Hilda gives 26 cards to Esther, Esther will have
35 as many cards as Hilda. How many cards does Esther have at first?
|
Case 1 |
Case 2 |
|
Esther |
Hilda |
Esther |
Hilda |
Before |
4 u + 24 |
20 u - 24 |
9 u - 26 |
15 u + 26 |
Change |
- 24 |
+ 24 |
+ 26 |
- 26 |
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 Esther had at first is the same in both cases.
9 u - 26 = 4 u + 24
9 u - 4 u = 24 + 26
5 u = 50
1 u = 10
Number of cards that Esther had at first
= 4 u + 24
= 4 x 10 + 24
= 40 + 24
= 64
Answer(s): 64