Henry and Pierre have some money. If Henry gives $394 to Pierre, the ratio of their money will be 3 : 5. If Henry gives $653 to Pierre, the ratio of their money will be 1: 4. How much does Henry have?
| |
Case 1 |
Case 2 |
| |
Henry |
Pierre |
Henry |
Pierre |
| Before |
15 u + $394 |
25 u - $394 |
8 u + $653 |
32 u - $653 |
| Change |
- $394 |
+ $394 |
- $653 |
+ $653 |
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 Henry has at first is the same in both cases.
15 u + 394 = 8 u + 653
15 u - 8 u = 653 - 394
7 u = 259
1 u = 259 ÷ 7 = 37
Amount that Henry has
= 15 u + 394
= 15 x 37 + 394
= 555 + 394
= $949
Answer(s): $949
