Bobby and Carl have some money. If Bobby gives $107 to Carl, the ratio of their money will be 2 : 5. If Bobby gives $509 to Carl, the ratio of their money will be 1: 4. How much does Bobby have?
|
Case 1 |
Case 2 |
|
Bobby |
Carl |
Bobby |
Carl |
Before |
10 u + $107 |
25 u - $107 |
7 u + $509 |
28 u - $509 |
Change |
- $107 |
+ $107 |
- $509 |
+ $509 |
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 + 107 = 7 u + 509
10 u - 7 u = 509 - 107
3 u = 402
1 u = 402 ÷ 3 = 134
Amount that Bobby has
= 10 u + 107
= 10 x 134 + 107
= 1340 + 107
= $1447
Answer(s): $1447