Emily and Zoe have some cards. If Emily gives 34 cards to Zoe, Zoe will have 3 times the number of cards as Emily. If Zoe gives 8 cards to Emily, Emily will have
23 as many cards as Zoe. How many cards does Emily have at first?
| |
Case 1 |
Case 2 |
| |
Emily |
Zoe |
Emily |
Zoe |
| Before |
5 u + 34 |
15 u - 34 |
8 u - 8 |
12 u + 8 |
| Change |
- 34 |
+ 34 |
+ 8 |
- 8 |
| 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 Emily had at first is the same in both cases.
8 u - 8 = 5 u + 34
8 u - 5 u = 34 + 8
3 u = 42
1 u = 14
Number of cards that Emily had at first
= 5 u + 34
= 5 x 14 + 34
= 70 + 34
= 104
Answer(s): 104
