SOLUTION: The sum of the reciprocals of two consecutive odd numbers is 8/15. Find the numbers.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The sum of the reciprocals of two consecutive odd numbers is 8/15. Find the numbers.       Log On


   

Question 667785: The sum of the reciprocals of two consecutive odd numbers is 8/15. Find the numbers.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If x is any odd number, then x and x+%2B+2 are consecutive odd numbers.
The sum of the reciprocals of two consecutive odd numbers is:
%281%2Fx%29%2B%281%2F%28x%2B2%29%29=8%2F15

%281%28x%2B2%29%2Fx%28x%2B2%29%29%2B%281x%2Fx%28x%2B2%29%29=8%2F15

%28%28x%2B2%2B1x%29%2Fx%28x%2B2%29%29=8%2F15

%282x%2B2%29%2F%28x%28x%2B2%29%29=8%2F15........cross multiply

15%282x%2B2%29=8%2Ax%28x%2B2%29

30x%2B30=8x%5E2%2B16x

0=8x%5E2-30x%2B16x-30

8x%5E2-14x-30=0.....replace -14x with 10x-24x

8x%5E2%2B10x-24x-30=0....group

%288x%5E2-24x%29%2B%2810x-30%29=0

8x%28x-3%29%2B10%28x-3%29=0

%288x%2B10%29%28x-3%29=0

solutions: positive solution

if x-3=0......=>.....x=3
the numbers are:
3 and 5

check:
%281%2Fx%29%2B%281%2F%28x%2B2%29%29=8%2F15
%281%2F3%29%2B%281%2F5%29=8%2F15
%281%2A5%2B1%2A3%29%2F15=8%2F15
%285%2B3%29%2F15=8%2F15
8%2F15=8%2F15