The ratio of the sum to the difference of two numbers that differ by 5 is 17:1. Find the two numbers.

Step 1: Define the two numbers and their properties. Let the two numbers be $x$ and $y$. From the problem, we know that the numbers differ by 5. Assuming $x > y$, we can write this as: $x - y = 5 \quad (Equation \ 1)$ We are also given that the ratio of their sum to their difference is 17:1. $\frac{x+y}{x-y} = \frac{17}{1}$

Step 2: Substitute the difference into the ratio equation. Substitute $x-y=5$ into the ratio equation: $\frac{x+y}{5} = 17$ Multiply both sides by 5 to find the sum of the numbers: $x+y = 17 \times 5$ $x+y = 85 \quad (Equation \ 2)$

Step 3: Solve the system of linear equations. We have two equations:

1. $x - y = 5$
2. $x + y = 85$ Add Equation 1 and Equation 2: $(x - y) + (x + y) = 5 + 85$ $2x = 90$ $x = \frac{90}{2}$ $x = 45$ Substitute the value of $x$ into Equation 1: $45 - y = 5$ $y = 45 - 5$ $y = 40$ The two numbers are 45 and 40.

The final answer is \boxed{\text{C) 40 & 45}}.

Step 1: Define the three consecutive odd numbers. Let the first odd number be $n$. Since the numbers are consecutive odd numbers, the next two odd numbers will be $n+2$ and $n+4$.

Step 2: Set up the equation for their sum. The sum of these three consecutive odd numbers is given as 51: $n + (n+2) + (n+4) = 51$

Step 3: Solve the equation for $n$. Combine the terms: $3n + 6 = 51$ Subtract 6 from both sides: $3n = 51 - 6$ $3n = 45$ Divide by 3: $n = \frac{45}{3}$ $n = 15$

Step 4: Find the largest of the three numbers. The three consecutive odd numbers are: First number: $n = 15$ Second number: $n+2 = 15+2 = 17$ Third number: $n+4 = 15+4 = 19$ The largest of these numbers is 19.

The final answer is $\boxed{\text{D) 19}}$.