Archie and Japheth have some money. If Archie gives $180 to Japheth, the ratio of their money will be 2 : 5. If Archie gives $483 to Japheth, the ratio of their money will be 1: 4. How much does Archie have?
| |
Case 1 |
Case 2 |
| |
Archie |
Japheth |
Archie |
Japheth |
| Before |
10 u + $180 |
25 u - $180 |
7 u + $483 |
28 u - $483 |
| Change |
- $180 |
+ $180 |
- $483 |
+ $483 |
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 + 180 = 7 u + 483
10 u - 7 u = 483 - 180
3 u = 303
1 u = 303 ÷ 3 = 101
Amount that Archie has
= 10 u + 180
= 10 x 101 + 180
= 1010 + 180
= $1190
Answer(s): $1190
