Daniel and Billy have some money. If Daniel gives $127 to Billy, the ratio of their money will be 2 : 5. If Daniel gives $589 to Billy, the ratio of their money will be 1: 4. How much does Daniel have?
| |
Case 1 |
Case 2 |
| |
Daniel |
Billy |
Daniel |
Billy |
| Before |
10 u + $127 |
25 u - $127 |
7 u + $589 |
28 u - $589 |
| Change |
- $127 |
+ $127 |
- $589 |
+ $589 |
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 Daniel has at first is the same in both cases.
10 u + 127 = 7 u + 589
10 u - 7 u = 589 - 127
3 u = 462
1 u = 462 ÷ 3 = 154
Amount that Daniel has
= 10 u + 127
= 10 x 154 + 127
= 1540 + 127
= $1667
Answer(s): $1667
