Mark and Archie have some money. If Mark gives $111 to Archie, the ratio of their money will be 2 : 5. If Mark gives $555 to Archie, the ratio of their money will be 1: 4. How much does Mark have?
| |
Case 1 |
Case 2 |
| |
Mark |
Archie |
Mark |
Archie |
| Before |
10 u + $111 |
25 u - $111 |
7 u + $555 |
28 u - $555 |
| Change |
- $111 |
+ $111 |
- $555 |
+ $555 |
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 Mark has at first is the same in both cases.
10 u + 111 = 7 u + 555
10 u - 7 u = 555 - 111
3 u = 444
1 u = 444 ÷ 3 = 148
Amount that Mark has
= 10 u + 111
= 10 x 148 + 111
= 1480 + 111
= $1591
Answer(s): $1591
