Billy and Fabian have some money. If Billy gives $225 to Fabian, the ratio of their money will be 3 : 5. If Billy gives $596 to Fabian, the ratio of their money will be 1: 4. How much does Billy have?
| |
Case 1 |
Case 2 |
| |
Billy |
Fabian |
Billy |
Fabian |
| Before |
15 u + $225 |
25 u - $225 |
8 u + $596 |
32 u - $596 |
| Change |
- $225 |
+ $225 |
- $596 |
+ $596 |
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 Billy has at first is the same in both cases.
15 u + 225 = 8 u + 596
15 u - 8 u = 596 - 225
7 u = 371
1 u = 371 ÷ 7 = 53
Amount that Billy has
= 15 u + 225
= 15 x 53 + 225
= 795 + 225
= $1020
Answer(s): $1020
