Harry and Archie have some money. If Harry gives $178 to Archie, the ratio of their money will be 2 : 5. If Harry gives $679 to Archie, the ratio of their money will be 1: 4. How much does Harry have?
| |
Case 1 |
Case 2 |
| |
Harry |
Archie |
Harry |
Archie |
| Before |
10 u + $178 |
25 u - $178 |
7 u + $679 |
28 u - $679 |
| Change |
- $178 |
+ $178 |
- $679 |
+ $679 |
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 Harry has at first is the same in both cases.
10 u + 178 = 7 u + 679
10 u - 7 u = 679 - 178
3 u = 501
1 u = 501 ÷ 3 = 167
Amount that Harry has
= 10 u + 178
= 10 x 167 + 178
= 1670 + 178
= $1848
Answer(s): $1848
