Fred and Tommy have some money. If Fred gives $205 to Tommy, the ratio of their money will be 2 : 5. If Fred gives $484 to Tommy, the ratio of their money will be 1: 4. How much does Fred have?
|
Case 1 |
Case 2 |
|
Fred |
Tommy |
Fred |
Tommy |
Before |
10 u + $205 |
25 u - $205 |
7 u + $484 |
28 u - $484 |
Change |
- $205 |
+ $205 |
- $484 |
+ $484 |
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 + 205 = 7 u + 484
10 u - 7 u = 484 - 205
3 u = 279
1 u = 279 ÷ 3 = 93
Amount that Fred has
= 10 u + 205
= 10 x 93 + 205
= 930 + 205
= $1135
Answer(s): $1135