Henry and David have some money. If Henry gives $346 to David, the ratio of their money will be 2 : 5. If Henry gives $634 to David, the ratio of their money will be 1: 4. How much does Henry have?
|
Case 1 |
Case 2 |
|
Henry |
David |
Henry |
David |
Before |
10 u + $346 |
25 u - $346 |
7 u + $634 |
28 u - $634 |
Change |
- $346 |
+ $346 |
- $634 |
+ $634 |
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 Henry has at first is the same in both cases.
10 u + 346 = 7 u + 634
10 u - 7 u = 634 - 346
3 u = 288
1 u = 288 ÷ 3 = 96
Amount that Henry has
= 10 u + 346
= 10 x 96 + 346
= 960 + 346
= $1306
Answer(s): $1306