Julie and Betty have some marbles. If Julie gives 39 marbles to Betty, Betty will have 5 times the number of marbles as Julie. If Betty gives 52 marbles to Julie, Julie will have
23 as many marbles as Betty. How many marbles does Julie have at first?
|
Case 1 |
Case 2 |
|
Julie |
Betty |
Julie |
Betty |
Before |
5 u + 39 |
25 u - 39 |
12 u - 52 |
18 u + 52 |
Change |
- 39 |
+ 39 |
+ 52 |
- 52 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 6 and 5 is 30.
Number of marbles that Julie had at first is the same in both cases.
12 u - 52 = 5 u + 39
12 u - 5 u = 39 + 52
7 u = 91
1 u = 13
Number of marbles that Julie had at first
= 5 u + 39
= 5 x 13 + 39
= 65 + 39
= 104
Answer(s): 104