George and Cody have some money. If George gives $316 to Cody, the ratio of their money will be 2 : 5. If George gives $469 to Cody, the ratio of their money will be 1: 4. How much does George have?
| |
Case 1 |
Case 2 |
| |
George |
Cody |
George |
Cody |
| Before |
10 u + $316 |
25 u - $316 |
7 u + $469 |
28 u - $469 |
| Change |
- $316 |
+ $316 |
- $469 |
+ $469 |
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 + 316 = 7 u + 469
10 u - 7 u = 469 - 316
3 u = 153
1 u = 153 ÷ 3 = 51
Amount that George has
= 10 u + 316
= 10 x 51 + 316
= 510 + 316
= $826
Answer(s): $826
