Paul and Ahmad have some money. If Paul gives $288 to Ahmad, the ratio of their money will be 2 : 5. If Paul gives $696 to Ahmad, the ratio of their money will be 1: 4. How much does Paul have?
| |
Case 1 |
Case 2 |
| |
Paul |
Ahmad |
Paul |
Ahmad |
| Before |
10 u + $288 |
25 u - $288 |
7 u + $696 |
28 u - $696 |
| Change |
- $288 |
+ $288 |
- $696 |
+ $696 |
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 + 288 = 7 u + 696
10 u - 7 u = 696 - 288
3 u = 408
1 u = 408 ÷ 3 = 136
Amount that Paul has
= 10 u + 288
= 10 x 136 + 288
= 1360 + 288
= $1648
Answer(s): $1648
