The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.
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Fraction = 4/7
Step-by-step explanation:
Let x be the numerator and y the denominator.
Fraction will be x/y.
Given:
(x + y) + 3 = 2y
x - y = -3 -------------(1)
(x -1) = (1/2)(y-1)
2x - y = 1 -------------(2)
Subtracting (2) from (1), we get: -x = -4
Therefore x = 4
Substituting in equation 1, we get 4 - y = -3
Therefore y = 7
Hence solved. x = 4, y = 7
So the fraction will be x/y = 4/7
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