Michael and Eric have some money. If Michael gives $381 to Eric, the ratio of their money will be 2 : 5. If Michael gives $678 to Eric, the ratio of their money will be 1: 4. How much does Michael have?
| |
Case 1 |
Case 2 |
| |
Michael |
Eric |
Michael |
Eric |
| Before |
10 u + $381 |
25 u - $381 |
7 u + $678 |
28 u - $678 |
| Change |
- $381 |
+ $381 |
- $678 |
+ $678 |
After
|
2x5 =
10 u |
5x5 =
25 u |
1x7 =
7 u |
4x7 =
28 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 7 and 5 is 35.
The amount that Michael has at first is the same in both cases.
10 u + 381 = 7 u + 678
10 u - 7 u = 678 - 381
3 u = 297
1 u = 297 ÷ 3 = 99
Amount that Michael has
= 10 u + 381
= 10 x 99 + 381
= 990 + 381
= $1371
Answer(s): $1371
