SOLUTION: The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers.
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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) (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:
The LCD is 60x(x+2), multiply everything by that.
cancel any matching numerators and denominators.
set = to 0
Factor
set each parentheses =0 and solve for x.
or
or
or
or
or
-12/11 is not an integer so reject it.
x=10
Therefore the first integer is:
and the second integer is
Sanity check:
does the reciprocal of 10 and 12 = 11/60?
We're right!!!
Happy Calculating!!!!
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