SOLUTION: The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers.
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Question 136649This 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 ankor@dixie-net.com(22740) (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.
:
Two consecutive even integers: x, (x+2)
:
+ =
;
Multiply equation by the common denominator, 60x(x+2)
60x(x+2)* + 60x(x+2)* = 60x(x+2)*
Cancel out the denominators and you have:
60(x+2) + 60x = 11x(x+2)
:
60x + 120 + 60x = 11x^2 + 22x
:
120x + 120 = 11x^2 + 22x
:
0 = 11x^2 + 22x - 120x - 120 = 0
A quadratic equation:
11x^2 - 98x - 120 = 0
Factors to:
(11x + 12)(x - 10) = 0
Two solutions:
11x = -12; not an integer
and
x = +10 and 12 are the consecutive integers
;
:
Check solution in original equation:
+ =
+ =
Using a common denominator of 60
+ =
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