Daniel and Albert have some money. If Daniel gives $379 to Albert, the ratio of their money will be 2 : 5. If Daniel gives $457 to Albert, the ratio of their money will be 1: 4. How much does Daniel have?
| |
Case 1 |
Case 2 |
| |
Daniel |
Albert |
Daniel |
Albert |
| Before |
10 u + $379 |
25 u - $379 |
7 u + $457 |
28 u - $457 |
| Change |
- $379 |
+ $379 |
- $457 |
+ $457 |
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 + 379 = 7 u + 457
10 u - 7 u = 457 - 379
3 u = 78
1 u = 78 ÷ 3 = 26
Amount that Daniel has
= 10 u + 379
= 10 x 26 + 379
= 260 + 379
= $639
Answer(s): $639
