Billy and Paul have some money. If Billy gives $105 to Paul, the ratio of their money will be 2 : 5. If Billy gives $471 to Paul, the ratio of their money will be 1: 4. How much does Billy have?
| |
Case 1 |
Case 2 |
| |
Billy |
Paul |
Billy |
Paul |
| Before |
10 u + $105 |
25 u - $105 |
7 u + $471 |
28 u - $471 |
| Change |
- $105 |
+ $105 |
- $471 |
+ $471 |
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 Billy has at first is the same in both cases.
10 u + 105 = 7 u + 471
10 u - 7 u = 471 - 105
3 u = 366
1 u = 366 ÷ 3 = 122
Amount that Billy has
= 10 u + 105
= 10 x 122 + 105
= 1220 + 105
= $1325
Answer(s): $1325
