Cathy and Betty have some coins. If Cathy gives 39 coins to Betty, Betty will have 4 times the number of coins as Cathy. If Betty gives 15 coins to Cathy, Cathy will have
25 as many coins as Betty. How many coins does Cathy have at first?
|
Case 1 |
Case 2 |
|
Cathy |
Betty |
Cathy |
Betty |
Before |
7 u + 39 |
28 u - 39 |
10 u - 15 |
25 u + 15 |
Change |
- 39 |
+ 39 |
+ 15 |
- 15 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 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 7 is 35.
Number of coins that Cathy had at first is the same in both cases.
10 u - 15 = 7 u + 39
10 u - 7 u = 39 + 15
3 u = 54
1 u = 18
Number of coins that Cathy had at first
= 7 u + 39
= 7 x 18 + 39
= 126 + 39
= 165
Answer(s): 165