Emily and Emma have some cards. If Emily gives 34 cards to Emma, Emma will have 5 times the number of cards as Emily. If Emma gives 85 cards to Emily, Emily will have
23 as many cards as Emma. How many cards does Emily have at first?
| |
Case 1 |
Case 2 |
| |
Emily |
Emma |
Emily |
Emma |
| Before |
5 u + 34 |
25 u - 34 |
12 u - 85 |
18 u + 85 |
| Change |
- 34 |
+ 34 |
+ 85 |
- 85 |
| After |
1x5 =
5 u |
5x5 =
25 u |
2x6 =
12 u |
3x6 =
18 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 5 is 30.
Number of cards that Emily had at first is the same in both cases.
12 u - 85 = 5 u + 34
12 u - 5 u = 34 + 85
7 u = 119
1 u = 17
Number of cards that Emily had at first
= 5 u + 34
= 5 x 17 + 34
= 85 + 34
= 119
Answer(s): 119
