Howard and David have some money. If Howard gives $384 to David, the ratio of their money will be 3 : 5. If Howard gives $622 to David, the ratio of their money will be 1: 4. How much does Howard have?
| |
Case 1 |
Case 2 |
| |
Howard |
David |
Howard |
David |
| Before |
15 u + $384 |
25 u - $384 |
8 u + $622 |
32 u - $622 |
| Change |
- $384 |
+ $384 |
- $622 |
+ $622 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Howard has at first is the same in both cases.
15 u + 384 = 8 u + 622
15 u - 8 u = 622 - 384
7 u = 238
1 u = 238 ÷ 7 = 34
Amount that Howard has
= 15 u + 384
= 15 x 34 + 384
= 510 + 384
= $894
Answer(s): $894
