Fred and Daniel have some money. If Fred gives $342 to Daniel, the ratio of their money will be 2 : 5. If Fred gives $516 to Daniel, the ratio of their money will be 1: 4. How much does Fred have?
| |
Case 1 |
Case 2 |
| |
Fred |
Daniel |
Fred |
Daniel |
| Before |
10 u + $342 |
25 u - $342 |
7 u + $516 |
28 u - $516 |
| Change |
- $342 |
+ $342 |
- $516 |
+ $516 |
After
|
2x5 =
10 u |
5x5 =
25 u |
1x7 =
7 u |
4x7 =
28 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 7 and 5 is 35.
The amount that Fred has at first is the same in both cases.
10 u + 342 = 7 u + 516
10 u - 7 u = 516 - 342
3 u = 174
1 u = 174 ÷ 3 = 58
Amount that Fred has
= 10 u + 342
= 10 x 58 + 342
= 580 + 342
= $922
Answer(s): $922
