SOLUTION: Find a fraction equivalent to 1/2 such that the product of the numerator and the denominator is 72.

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Question 34439This question is from textbook Modern Mathematics for Elementary Educators
: Find a fraction equivalent to 1/2 such that the product of the numerator and the denominator is 72.This question is from textbook Modern Mathematics for Elementary Educators

Found 3 solutions by mukhopadhyay, Earlsdon, Prithwis:
Answer by mukhopadhyay(490) About Me  (Show Source):
You can put this solution on YOUR website!
x/(72-x) = 1/2
=> 2x = 72-x
=> 3x = 72
=> x = 24

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Try this: Let x = the numerator and y = the denominator.
x%2Fy+=+1%2F2 Rewrite this as: y+=+2x and substitute below.
x%2Ay+=+72
x%282x%29+=+72 Solve for x.
2x%5E2+=+72 Divide both sides buy 2.
x%5E2+=+36 Take the square root of both sides.
x = +or-6
y = 2x
y = +or-12
There are two answers:
6%2F12+=+1%2F2
%28-6%29%2F%28-12%29+=+1%2F2
In both of these fractions, the product of the numerator (6 or -6) and the denominator (12 or -12) = 72

Answer by Prithwis(166) About Me  (Show Source):
You can put this solution on YOUR website!
If numerator is x, the denominator is 72/x
x/(72/x) = 1/2
=> x^2 = 36
=> x = +6 or x = -6