Bobby and Pierre have some money. If Bobby gives $180 to Pierre, the ratio of their money will be 2 : 5. If Bobby gives $684 to Pierre, the ratio of their money will be 1: 4. How much does Bobby have?
| |
Case 1 |
Case 2 |
| |
Bobby |
Pierre |
Bobby |
Pierre |
| Before |
10 u + $180 |
25 u - $180 |
7 u + $684 |
28 u - $684 |
| Change |
- $180 |
+ $180 |
- $684 |
+ $684 |
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 Bobby has at first is the same in both cases.
10 u + 180 = 7 u + 684
10 u - 7 u = 684 - 180
3 u = 504
1 u = 504 ÷ 3 = 168
Amount that Bobby has
= 10 u + 180
= 10 x 168 + 180
= 1680 + 180
= $1860
Answer(s): $1860
