Andy and Mark have some money. If Andy gives $205 to Mark, the ratio of their money will be 2 : 5. If Andy gives $667 to Mark, the ratio of their money will be 1: 4. How much does Andy have?
| |
Case 1 |
Case 2 |
| |
Andy |
Mark |
Andy |
Mark |
| Before |
10 u + $205 |
25 u - $205 |
7 u + $667 |
28 u - $667 |
| Change |
- $205 |
+ $205 |
- $667 |
+ $667 |
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 Andy has at first is the same in both cases.
10 u + 205 = 7 u + 667
10 u - 7 u = 667 - 205
3 u = 462
1 u = 462 ÷ 3 = 154
Amount that Andy has
= 10 u + 205
= 10 x 154 + 205
= 1540 + 205
= $1745
Answer(s): $1745
