Final answer:
To find the two numbers, we can set up two equations based on the given information and then solve for the unknowns. By solving the equations, we find that the two numbers are 6 and 9.
Step-by-step explanation:
To find the two numbers, let's call them x and y. We are given that the numbers differ by 3, so we can write one equation as x - y = 3. Another equation can be written based on the given information that the sum of their reciprocals is 1/10, which can be written as 1/x + 1/y = 1/10.
We can solve these two equations using the method of substitution or elimination. In this case, let's solve by substitution. We can rearrange the first equation to express x in terms of y, giving x = y + 3.
Substituting this value of x into the second equation, we get (1/(y + 3)) + (1/y) = 1/10. We can then simplify and solve for y. After finding y, we can substitute its value into the first equation to find x. Solving the equations, we find that the two numbers are 6 and 9. Therefore, the answer is B. 6 and 9.