Erika and Fanny have some marbles. If Erika gives 15 marbles to Fanny, Fanny will have 3 times the number of marbles as Erika. If Fanny gives 3 marbles to Erika, Erika will have
23 as many marbles as Fanny. How many marbles does Erika have at first?
| |
Case 1 |
Case 2 |
| |
Erika |
Fanny |
Erika |
Fanny |
| Before |
5 u + 15 |
15 u - 15 |
8 u - 3 |
12 u + 3 |
| Change |
- 15 |
+ 15 |
+ 3 |
- 3 |
| After |
1x5 =
5 u |
3x5 =
15 u |
2x4 =
8 u |
3x4 =
12 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 4 and 5 is 20.
Number of marbles that Erika had at first is the same in both cases.
8 u - 3 = 5 u + 15
8 u - 5 u = 15 + 3
3 u = 18
1 u = 6
Number of marbles that Erika had at first
= 5 u + 15
= 5 x 6 + 15
= 30 + 15
= 45
Answer(s): 45
