Eva and Emma have some marbles. If Eva gives 12 marbles to Emma, Emma will have 5 times the number of marbles as Eva. If Emma gives 68 marbles to Eva, Eva will have
35 as many marbles as Emma. How many marbles does Eva have at first?
|
Case 1 |
Case 2 |
|
Eva |
Emma |
Eva |
Emma |
Before |
4 u + 12 |
20 u - 12 |
9 u - 68 |
15 u + 68 |
Change |
- 12 |
+ 12 |
+ 68 |
- 68 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 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 8 is 24.
Number of marbles that Eva had at first is the same in both cases.
9 u - 68 = 4 u + 12
9 u - 4 u = 12 + 68
5 u = 80
1 u = 16
Number of marbles that Eva had at first
= 4 u + 12
= 4 x 16 + 12
= 64 + 12
= 76
Answer(s): 76