Final answer:
To solve this problem, assign variables to the three numbers and set up equations based on the given information. Then, simplify and solve the equations to find the values of the numbers. The correct answer is x = 20, y = 24, and z = 38.
Step-by-step explanation:
To solve this problem, let's assign variables to the three numbers. Let x be the first number, y be the second number, and z be the third number.
According to the problem, the sum of the three numbers is 82, so we can write the equation: x + y + z = 82.
The third number is 8 more than the first, so we can write the equation: z = x + 8.
The second number is four times the third, so we can write the equation: y = 4z.
Now, we can substitute the third equation into the second equation to get: y = 4(x + 8).
Substituting the second and third equations into the first equation, we get: x + 4(x + 8) + (x + 8) = 82.
Simplifying and solving this equation, we find that x = 20, y = 24, and z = 38.
Therefore, the correct answer is option b: x = 20, y = 24, and z = 38.