Hazel and Natalie have some cards. If Hazel gives 28 cards to Natalie, Natalie will have 3 times the number of cards as Hazel. If Natalie gives 11 cards to Hazel, Hazel will have
23 as many cards as Natalie. How many cards does Hazel have at first?
|
Case 1 |
Case 2 |
|
Hazel |
Natalie |
Hazel |
Natalie |
Before |
5 u + 28 |
15 u - 28 |
8 u - 11 |
12 u + 11 |
Change |
- 28 |
+ 28 |
+ 11 |
- 11 |
After |
1x5 = 5 u |
3x5 = 15 u |
2x4 = 8 u |
3x4 = 12 u |
The total number of cards in both cases remains unchanged. Make the total number of cards in both cases the same. LCM of 4 and 5 is 20.
Number of cards that Hazel had at first is the same in both cases.
8 u - 11 = 5 u + 28
8 u - 5 u = 28 + 11
3 u = 39
1 u = 13
Number of cards that Hazel had at first
= 5 u + 28
= 5 x 13 + 28
= 65 + 28
= 93
Answer(s): 93