Math

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.

  1. 👍 0
  2. 👎 0
  3. 👁 1,786
  1. x = first number

    x + 1 = second number

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

    [ 1 * ( x + 1 ) + 1 * x ] / [ x * ( x + 1 ) ] = 17 / 72

    [ ( x + 1 ) + x ] / [ x * x + x * 1 ) ] = 17 / 72

    ( 2 x + 1 ) / ( x ^ 2 + x ) = 17 / 72 Multiply both sides by 72

    72 * ( 2 x + 1 ) / ( x ^ 2 + x ) = 17

    ( 72 * 2 x + 72 * 1 ) / ( x ^ 2 + x ) = 17

    ( 144 x + 72 ) / ( x ^ 2 + x ) = 17 Multiply both sides by x ^ 2 + x

    144 x + 72 = 17 * ( x ^ 2 + x )

    144 x + 72 = 17 * x ^ 2 + 17 * x

    144 x + 72 = 17 x ^ 2 + 17 x Subtract 144 x to both sides

    144 x + 72 - 144 x = 17 x ^ 2 + 17 x - 144 x

    72 = 17 x ^ 2 - 127 x Subtract 72 to both sides

    72 - 72 = 17 x ^ 2 - 127 x - 72

    0 = 17 x ^ 2 - 127 x - 72

    17 x ^ 2 - 127 x - 72 = 0

    The solutions are:

    x = - 9 / 17 and x = 8

    - 9 / 17 isn't positive integers so x = 8

    first number = 8

    second number = 8 + 1 = 9

    Proof:

    1 / x + 1 / ( x + 1 ) =

    1 / 8 + 1 / 9 =

    ( 1 * 9 + 1 * 8 ) / ( 8 * 9 ) =

    ( 9 + 8 ) / 72 = 17 / 72

    1. 👍 1
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    [2.05] Choose the equation that could be used to find two consecutive integers whose sum is 69.

  2. Math

    Three consecutive integers have a sum of 357. Fid the integers algebraically. I know the three numbers are 118, 119, and 120 but how do you write it in an algebraic expression ?

  3. Algebra

    The sum of two consecutive odd integers is 24. Which equation can be used to find the first integer n? F. n + 1=24 G. n + 2=24 H. 2n + 1=24 I. 2n + 2=24

  4. Math

    The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!

  1. Math

    The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking

  2. Algebra 2

    The sum of the reciprocals of two consecutive even integers is 9/40. this can be represented by the equation shown. (1/x)+(1/x+2)=9/40 Use the rational equation to determine the integers. Please help!! I have no idea what to do:(

  3. algebra

    Five times the smallest of three consecutive odd integers is ten more than twice the longest. Find the integers. The sum of three integers is one hundred twenty three more than the first number. The second number is two more than

  4. smallest of 3 integers

    The sum of the reciprocals of three consecutive positive integers is equal to 47 divided by the product of the integers. What is the smallest of the three integers?

  1. math

    the sum of the square of two consecutive positive integers is 265.what are the integers?

  2. Algebra

    The sum of two consecutive even integers is 118. A. Define a variable for the smaller integer. B. What must you add to an even integer to get the next greater even integer? C. Write an expression for the second integer. D. Write

  3. algebra homework help

    The sum of two consecutive integers is 285 How would I solve an equation like this

  4. math

    The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work.

You can view more similar questions or ask a new question.