Fiona and Barbara have some coins. If Fiona gives 23 coins to Barbara, Barbara will have 5 times the number of coins as Fiona. If Barbara gives 47 coins to Fiona, Fiona will have
23 as many coins as Barbara. How many coins does Fiona have at first?
|
Case 1 |
Case 2 |
|
Fiona |
Barbara |
Fiona |
Barbara |
Before |
5 u + 23 |
25 u - 23 |
12 u - 47 |
18 u + 47 |
Change |
- 23 |
+ 23 |
+ 47 |
- 47 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 u |
The total number of coins in both cases remains unchanged. Make the total number of coins in both cases the same. LCM of 6 and 5 is 30.
Number of coins that Fiona had at first is the same in both cases.
12 u - 47 = 5 u + 23
12 u - 5 u = 23 + 47
7 u = 70
1 u = 10
Number of coins that Fiona had at first
= 5 u + 23
= 5 x 10 + 23
= 50 + 23
= 73
Answer(s): 73