Seth and Brandon have some money. If Seth gives $317 to Brandon, the ratio of their money will be 3 : 5. If Seth gives $499 to Brandon, the ratio of their money will be 1: 4. How much does Seth have?
| |
Case 1 |
Case 2 |
| |
Seth |
Brandon |
Seth |
Brandon |
| Before |
15 u + $317 |
25 u - $317 |
8 u + $499 |
32 u - $499 |
| Change |
- $317 |
+ $317 |
- $499 |
+ $499 |
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 Seth has at first is the same in both cases.
15 u + 317 = 8 u + 499
15 u - 8 u = 499 - 317
7 u = 182
1 u = 182 ÷ 7 = 26
Amount that Seth has
= 15 u + 317
= 15 x 26 + 317
= 390 + 317
= $707
Answer(s): $707
