Dana and Rachel have some coins. If Dana gives 15 coins to Rachel, Rachel will have 4 times the number of coins as Dana. If Rachel gives 15 coins to Dana, Dana will have
12 as many coins as Rachel. How many coins does Dana have at first?
|
Case 1 |
Case 2 |
|
Dana |
Rachel |
Dana |
Rachel |
Before |
3 u + 15 |
12 u - 15 |
5 u - 15 |
10 u + 15 |
Change |
- 15 |
+ 15 |
+ 15 |
- 15 |
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 Dana had at first is the same in both cases.
5 u - 15 = 3 u + 15
5 u - 3 u = 15 + 15
2 u = 30
1 u = 15
Number of coins that Dana had at first
= 3 u + 15
= 3 x 15 + 15
= 45 + 15
= 60
Answer(s): 60