Question

the sum of the reciprocal of two consecutive positive integers is 17/72. Write an equation that can be used to find the two integers. What are the integers?

Answer 1

`(1)/(x)+(1)/(x+1)=(17)/(72)`

The two consecutive positive integers are 8 and 9.

Step-by-step explanation:

Let the 1st positive integer be x and the 2nd be x + 1, so their reciprocal will be 1/x and 1/x+1.

The equation can then be written as;

`(1)/(x)+(1)/(x+1)=(17)/(72)`

To solve for x, the 1st step is to find the LCM of the left-hand side of the equation;

`\begin{gathered} ((x+1)+x)/(x(x+1))=(17)/(72) \\ (2x+1)/(x(x+1))=(17)/(72) \end{gathered}`

We can equate the numerators and solve for x as shown below;

`\begin{gathered} 2x+1=17 \\ 2x=17-1 \\ x=(16)/(2) \\ x=8 \end{gathered}`

If the 1st positive integer, x, is 8, therefore the 2nd integer, x + 1, will be;

`x+1=8+1=9`