Question

2. The sum of the reciprocals of two consecutive positive integers is 17/72. Write an equation that can be used to find the two integers. What are the integers?
Steve helped me yesterday and gave me the hint 8+9=17. Then I thought about it and saw 8*9=72, but I am confused about how to put it into an equation.

Answer 1

To answer this item, we let x be the first positive integer. Then, the second would be x+1. Their reciprocals would be 1/x and 1/(x+1). Then, the equation that would best represent the scenario above is,
                            1/x + 1/(x+1) = 17/72
Solving the equation above,
                           ((x+1) + x) / (x)(x+1) = 17/72
If we take the numerators of both sides of the equation,
                              (x+1) + x = 17
The value of x from the equation is 8 and x+1 would be 9. Thus, the answer would be 8 and 9.