Question

the numerator of a fraction is one less than its denominator . if three is added to each of the numerator and denominator, the fraction is increased by 3/28. find the fraction.​

Answer 1

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kamahujhtna

07.02.2016

Math

Secondary School

+10 pts

Answered

The numerator of a fraction is one less than its denominator . If three is added to each of the numerator and denominator , then the fraction is increased by 3/28 . Find the fraction .

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nikitasingh79 Genius

Let the Denominator = x

numerator = (x-1)

fraction = numerator/denominator

Fraction = x-1/x

A.T.Q

x-1+3/x+3 = x-1/x + 3/28

x+2/x+3 = 28x - 28 + 3x/ 28x

28x(x+2) = (31x - 28)(x+3)

28x² + 56x = 31x² - 28x + 93x - 84

31x² - 28x² + 93x - 28x - 56x - 84

3x² + 9x - 84

[ Divide by 3]

x²+ 3x - 28

x²+ 7x - 4x - 28

x(x+7) -4(x+7)

(x-4) (x+7)

x = 4 or -7 [x is a natural number, x>0]

Hence , x= 4

Fraction = x-1/ x = 4-1 /4 = ¾

Hence, the fraction is 3/4