Daniel and David have some money. If Daniel gives $184 to David, the ratio of their money will be 2 : 5. If Daniel gives $688 to David, the ratio of their money will be 1: 4. How much does Daniel have?
| |
Case 1 |
Case 2 |
| |
Daniel |
David |
Daniel |
David |
| Before |
10 u + $184 |
25 u - $184 |
7 u + $688 |
28 u - $688 |
| Change |
- $184 |
+ $184 |
- $688 |
+ $688 |
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 + 184 = 7 u + 688
10 u - 7 u = 688 - 184
3 u = 504
1 u = 504 ÷ 3 = 168
Amount that Daniel has
= 10 u + 184
= 10 x 168 + 184
= 1680 + 184
= $1864
Answer(s): $1864
