Fred and Jack have some money. If Fred gives $364 to Jack, the ratio of their money will be 3 : 5. If Fred gives $511 to Jack, the ratio of their money will be 1: 4. How much does Fred have?
| |
Case 1 |
Case 2 |
| |
Fred |
Jack |
Fred |
Jack |
| Before |
15 u + $364 |
25 u - $364 |
8 u + $511 |
32 u - $511 |
| Change |
- $364 |
+ $364 |
- $511 |
+ $511 |
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 Fred has at first is the same in both cases.
15 u + 364 = 8 u + 511
15 u - 8 u = 511 - 364
7 u = 147
1 u = 147 ÷ 7 = 21
Amount that Fred has
= 15 u + 364
= 15 x 21 + 364
= 315 + 364
= $679
Answer(s): $679
