Archie and Seth have some money. If Archie gives $375 to Seth, the ratio of their money will be 2 : 5. If Archie gives $663 to Seth, the ratio of their money will be 1: 4. How much does Archie have?
| |
Case 1 |
Case 2 |
| |
Archie |
Seth |
Archie |
Seth |
| Before |
10 u + $375 |
25 u - $375 |
7 u + $663 |
28 u - $663 |
| Change |
- $375 |
+ $375 |
- $663 |
+ $663 |
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 + 375 = 7 u + 663
10 u - 7 u = 663 - 375
3 u = 288
1 u = 288 ÷ 3 = 96
Amount that Archie has
= 10 u + 375
= 10 x 96 + 375
= 960 + 375
= $1335
Answer(s): $1335
