Archie and George have some money. If Archie gives $349 to George, the ratio of their money will be 3 : 5. If Archie gives $538 to George, the ratio of their money will be 1: 4. How much does Archie have?
| |
Case 1 |
Case 2 |
| |
Archie |
George |
Archie |
George |
| Before |
15 u + $349 |
25 u - $349 |
8 u + $538 |
32 u - $538 |
| Change |
- $349 |
+ $349 |
- $538 |
+ $538 |
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 Archie has at first is the same in both cases.
15 u + 349 = 8 u + 538
15 u - 8 u = 538 - 349
7 u = 189
1 u = 189 ÷ 7 = 27
Amount that Archie has
= 15 u + 349
= 15 x 27 + 349
= 405 + 349
= $754
Answer(s): $754
