Archie and Harry have some money. If Archie gives $273 to Harry, the ratio of their money will be 2 : 5. If Archie gives $552 to Harry, the ratio of their money will be 1: 4. How much does Archie have?
| |
Case 1 |
Case 2 |
| |
Archie |
Harry |
Archie |
Harry |
| Before |
10 u + $273 |
25 u - $273 |
7 u + $552 |
28 u - $552 |
| Change |
- $273 |
+ $273 |
- $552 |
+ $552 |
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 + 273 = 7 u + 552
10 u - 7 u = 552 - 273
3 u = 279
1 u = 279 ÷ 3 = 93
Amount that Archie has
= 10 u + 273
= 10 x 93 + 273
= 930 + 273
= $1203
Answer(s): $1203
