Question 842441: Please Help!
The sum of the reciprocal of two positive numbers is 1/9, and one of the numbers is 3 times the other. find the numbers
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = one of the numbers.
let 3x = the other number.
the reciprocal of x is equal to 1/x.
the reciprocal of 3x is equal to 1/3x
the sum of the reciprocals of the number is equal to 1/9.
your equation is:
1/x + 1/3x = 1/9
multiply both sides of this equation by 3x to get:
3 + 1 = 3x/9
simplify to get 4 = 3x/9
multiply both sides of this equation by 9 to get:
36 = 3x
divide both sides of this equation by 3 to get:
12 = x
that should be your answer.
x = 12
one of the number is equal to 12.
the other number is equal to 3*12 - 36.
the sum of the reciprocals of these number should be equal to 1/9.
the reciprocal of 12 is 1/12.
the reciprocal of 36 is 1/36.
you get:
1/12 + 1/36 = 1/9
a common denominator would be equal to 36 since 12 goes into 36
converting the left side of the equation to common denominators, your equation becomes:
3/36 + 1/36 = 1/9
combine like terms to get:
4/36 = 1/9
if you multiply the right side of the equation by 4/4, you get:
4/36 = 4/36 which is true, confirming that the value of x = 12 is good.
your numbers are 12 and 36.
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