George and Ben have some money. If George gives $246 to Ben, the ratio of their money will be 2 : 5. If George gives $657 to Ben, the ratio of their money will be 1: 4. How much does George have?
|
Case 1 |
Case 2 |
|
George |
Ben |
George |
Ben |
Before |
10 u + $246 |
25 u - $246 |
7 u + $657 |
28 u - $657 |
Change |
- $246 |
+ $246 |
- $657 |
+ $657 |
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 George has at first is the same in both cases.
10 u + 246 = 7 u + 657
10 u - 7 u = 657 - 246
3 u = 411
1 u = 411 ÷ 3 = 137
Amount that George has
= 10 u + 246
= 10 x 137 + 246
= 1370 + 246
= $1616
Answer(s): $1616