SOLUTION: The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 67915This question is from textbook Algebra:Structure and Method
: The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers. This question is from textbook Algebra:Structure and Method

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers.
Let the first even integer be:x
Then the next even integer is: x+2
The reciprocal of x=1/x
The reciprocal of x+2=1/(x+2)
Sum means add:
1%2Fx%2B1%2F%28x%2B2%29=11%2F60 The LCD is 60x(x+2), multiply everything by that.
60x%28x%2B2%29%2A1%2Fx%2B60x%28x%2B2%29%2A1%2F%28x%2B2%29=60x%28x%2B2%29%2A11%2F60 cancel any matching numerators and denominators.
60%28x%2B2%29%2B60x=11x%28x%2B2%29
60x%2B120%2B60x=11x%5E2%2B22x
120x%2B120=11x%5E2%2B22x set = to 0
120x-120x%2B120-120=11x%5E2%2B22x-120x-120
0=11x%5E2-98x-120 Factor
0=11x%5E2-110x%2B12x-120
0=11x%28x-10%29%2B12%28x-10%29
0=%2811x%2B12%29%28x-10%29 set each parentheses =0 and solve for x.
11x%2B12=0 or x-10=0
11x%2B12-12=0-12 or x-10%2B10=0%2B10
11x=-12 or x=10
11x%2F11=-12%2F11 or x=10
x=-12%2F11 or x=10
-12/11 is not an integer so reject it.
x=10
Therefore the first integer is: highlight%28x=10%29
and the second integer is highlight%28x%2B2=10%2B2=12%29
Sanity check:
does the reciprocal of 10 and 12 = 11/60?
1%2F10%2B1%2F12=11%2F60
6%2F60%2B5%2F60=11%2F60
11%2F60=11%2F60 We're right!!!
Happy Calculating!!!!