Vincent and Luke have some money. If Vincent gives $323 to Luke, the ratio of their money will be 3 : 5. If Vincent gives $561 to Luke, the ratio of their money will be 1: 4. How much does Vincent have?
| |
Case 1 |
Case 2 |
| |
Vincent |
Luke |
Vincent |
Luke |
| Before |
15 u + $323 |
25 u - $323 |
8 u + $561 |
32 u - $561 |
| Change |
- $323 |
+ $323 |
- $561 |
+ $561 |
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 Vincent has at first is the same in both cases.
15 u + 323 = 8 u + 561
15 u - 8 u = 561 - 323
7 u = 238
1 u = 238 ÷ 7 = 34
Amount that Vincent has
= 15 u + 323
= 15 x 34 + 323
= 510 + 323
= $833
Answer(s): $833
