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.
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.
