Emily and Fanny have some coins. If Emily gives 10 coins to Fanny, Fanny will have 4 times the number of coins as Emily. If Fanny gives 10 coins to Emily, Emily will have
12 as many coins as Fanny. How many coins does Emily have at first?
|
Case 1 |
Case 2 |
|
Emily |
Fanny |
Emily |
Fanny |
Before |
3 u + 10 |
12 u - 10 |
5 u - 10 |
10 u + 10 |
Change |
- 10 |
+ 10 |
+ 10 |
- 10 |
After |
1x3 = 3 u |
4x3 = 12 u |
1x5 = 5 u |
2x5 = 10 u |
The total number of coins in both cases remains unchanged. Make the total number of coins in both cases the same. LCM of 5 and 3 is 15.
Number of coins that Emily had at first is the same in both cases.
5 u - 10 = 3 u + 10
5 u - 3 u = 10 + 10
2 u = 20
1 u = 10
Number of coins that Emily had at first
= 3 u + 10
= 3 x 10 + 10
= 30 + 10
= 40
Answer(s): 40