Paul and Peter have some money. If Paul gives $350 to Peter, the ratio of their money will be 2 : 5. If Paul gives $524 to Peter, the ratio of their money will be 1: 4. How much does Paul have?
| |
Case 1 |
Case 2 |
| |
Paul |
Peter |
Paul |
Peter |
| Before |
10 u + $350 |
25 u - $350 |
7 u + $524 |
28 u - $524 |
| Change |
- $350 |
+ $350 |
- $524 |
+ $524 |
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 Paul has at first is the same in both cases.
10 u + 350 = 7 u + 524
10 u - 7 u = 524 - 350
3 u = 174
1 u = 174 ÷ 3 = 58
Amount that Paul has
= 10 u + 350
= 10 x 58 + 350
= 580 + 350
= $930
Answer(s): $930
