Michael and Fred have some money. If Michael gives $136 to Fred, the ratio of their money will be 2 : 5. If Michael gives $508 to Fred, the ratio of their money will be 1: 4. How much does Michael have?
|
Case 1 |
Case 2 |
|
Michael |
Fred |
Michael |
Fred |
Before |
10 u + $136 |
25 u - $136 |
7 u + $508 |
28 u - $508 |
Change |
- $136 |
+ $136 |
- $508 |
+ $508 |
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 + 136 = 7 u + 508
10 u - 7 u = 508 - 136
3 u = 372
1 u = 372 ÷ 3 = 124
Amount that Michael has
= 10 u + 136
= 10 x 124 + 136
= 1240 + 136
= $1376
Answer(s): $1376