Archie and Perry have some money. If Archie gives $216 to Perry, the ratio of their money will be 2 : 5. If Archie gives $456 to Perry, the ratio of their money will be 1: 4. How much does Archie have?
| |
Case 1 |
Case 2 |
| |
Archie |
Perry |
Archie |
Perry |
| Before |
10 u + $216 |
25 u - $216 |
7 u + $456 |
28 u - $456 |
| Change |
- $216 |
+ $216 |
- $456 |
+ $456 |
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 Archie has at first is the same in both cases.
10 u + 216 = 7 u + 456
10 u - 7 u = 456 - 216
3 u = 240
1 u = 240 ÷ 3 = 80
Amount that Archie has
= 10 u + 216
= 10 x 80 + 216
= 800 + 216
= $1016
Answer(s): $1016
