The sum of the reciprocal of a number and 5 is equal to 8. What is the number?

To solve the problem, we start with the equation derived from the information given. The problem states that the sum of the reciprocal of a number and 5 equals 8. Let's denote the number as ( x ). Therefore, we can set up the following equation:

[

\frac{1}{x} + 5 = 8

]

Next, we isolate the reciprocal of the number:

[

\frac{1}{x} = 8 - 5

]

Calculating the right side:

[

\frac{1}{x} = 3

]

Now, to find ( x ), we take the reciprocal of both sides:

[

x = \frac{1}{3}

]

This solution aligns with the given answer choice. The essence of this problem is understanding how to manipulate the equation involving a reciprocal. In this case, correctly isolating the variable led to finding the number that satisfies the given condition. The option of ( \frac{1}{3} ) is indeed the only valid solution to the equation presented in the problem.