Owen and Henry have some money. If Owen gives $144 to Henry, the ratio of their money will be 3 : 5. If Owen gives $613 to Henry, the ratio of their money will be 1: 4. How much does Owen have?
| |
Case 1 |
Case 2 |
| |
Owen |
Henry |
Owen |
Henry |
| Before |
15 u + $144 |
25 u - $144 |
8 u + $613 |
32 u - $613 |
| Change |
- $144 |
+ $144 |
- $613 |
+ $613 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Owen has at first is the same in both cases.
15 u + 144 = 8 u + 613
15 u - 8 u = 613 - 144
7 u = 469
1 u = 469 ÷ 7 = 67
Amount that Owen has
= 15 u + 144
= 15 x 67 + 144
= 1005 + 144
= $1149
Answer(s): $1149
