Vincent and Howard have some money. If Vincent gives $380 to Howard, the ratio of their money will be 3 : 5. If Vincent gives $674 to Howard, the ratio of their money will be 1: 4. How much does Vincent have?
| |
Case 1 |
Case 2 |
| |
Vincent |
Howard |
Vincent |
Howard |
| Before |
15 u + $380 |
25 u - $380 |
8 u + $674 |
32 u - $674 |
| Change |
- $380 |
+ $380 |
- $674 |
+ $674 |
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 + 380 = 8 u + 674
15 u - 8 u = 674 - 380
7 u = 294
1 u = 294 ÷ 7 = 42
Amount that Vincent has
= 15 u + 380
= 15 x 42 + 380
= 630 + 380
= $1010
Answer(s): $1010
