Min and Erika have some marbles. If Min gives 18 marbles to Erika, Erika will have 4 times the number of marbles as Min. If Erika gives 18 marbles to Min, Min will have
12 as many marbles as Erika. How many marbles does Min have at first?
|
Case 1 |
Case 2 |
|
Min |
Erika |
Min |
Erika |
Before |
3 u + 18 |
12 u - 18 |
5 u - 18 |
10 u + 18 |
Change |
- 18 |
+ 18 |
+ 18 |
- 18 |
After |
1x3 = 3 u |
4x3 = 12 u |
1x5 = 5 u |
2x5 = 10 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 5 and 3 is 15.
Number of marbles that Min had at first is the same in both cases.
5 u - 18 = 3 u + 18
5 u - 3 u = 18 + 18
2 u = 36
1 u = 18
Number of marbles that Min had at first
= 3 u + 18
= 3 x 18 + 18
= 54 + 18
= 72
Answer(s): 72