Final answer:
To determine the ages of Bob and Carl, we set c as Carl's age and derived the equation c + (c + 6) = 56. Solving this equation gave us Carl's age as 25 and Bob's age as 31 years old.
Step-by-step explanation:
The problem presents us with a system of linear equations concerning the ages of two brothers, Bob and Carl. We are given that Bob is 6 years older than Carl and that the sum of their ages is 56 years. To find their ages, we can set up the equations based on the information provided.
Let's denote Carl's age as c years. Therefore, Bob's age will be c + 6 years. According to the problem, the sum of their ages is 56, leading to our main equation: c + (c + 6) = 56.
To find the value of c, we need to solve the equation:
- Combine like terms: 2c + 6 = 56
- Subtract 6 from both sides: 2c = 50
- Divide both sides by 2 to get Carl's age: c = 25
Now that we have Carl's age, we can find Bob's age by adding 6:
Hence, Carl is 25 years old, and Bob is 31 years old.