Final answer:
The problem is solved by setting up an equation where x represents the smaller number and x + 17 represents the larger number. Solving for x gives us the smaller number as 24, and adding 17 to it gives us the larger number, which is 41, corresponding to option C.
Step-by-step explanation:
The question involves a basic algebra problem where we need to find two numbers that add up to a sum of 65, with the condition that the larger number is 17 more than the smaller number.
Let us denote the smaller number as x and the larger number as x + 17. According to the problem, when we add these two numbers together, their sum is 65. This gives us the equation:
x + (x + 17) = 65
Combining like terms we get:
2x + 17 = 65
Subtracting 17 from both sides:
2x = 48
Dividing both sides by 2:
x = 24
Therefore, the smaller number is 24, and the larger number is x + 17, which is 24 + 17 = 41.
So, the correct answer to the problem is option C, which is 41.