Owen and Michael have some money. If Owen gives $250 to Michael, the ratio of their money will be 2 : 5. If Owen gives $646 to Michael, the ratio of their money will be 1: 4. How much does Owen have?
| |
Case 1 |
Case 2 |
| |
Owen |
Michael |
Owen |
Michael |
| Before |
10 u + $250 |
25 u - $250 |
7 u + $646 |
28 u - $646 |
| Change |
- $250 |
+ $250 |
- $646 |
+ $646 |
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 Owen has at first is the same in both cases.
10 u + 250 = 7 u + 646
10 u - 7 u = 646 - 250
3 u = 396
1 u = 396 ÷ 3 = 132
Amount that Owen has
= 10 u + 250
= 10 x 132 + 250
= 1320 + 250
= $1570
Answer(s): $1570
