Question

the sum of numerator you and denominator of fraction is 3 less than twice the denominator. if the numerator and denominator are decreased by 1 the numerator become half the denominator. determine the fraction
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Answer 1

Let the fraction be x/y, then according to question:

➵ x + y = 2y - 3

➵ x - y = - 3 __(i)

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If the numerator and denominator are decreased by 1 the numerator become half the denominator, then

➵ x - 1 = ½(y - 1)

➵ 2x - 2 = y - 1

➵ 2x - y = 1 __(ii)

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On multiplying equation (i) by 2,

➵ 2x - 2y = - 6 __(iii)

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On doing (ii) - (iii),

➵ y = 7

Hence, x - y = - 3

➵ x = 4

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Answer

➵ x = 4 and y = 7

Hence fraction = 4/7

Answer 2

Answer:

x = 4 and y = 7

Therefore, fraction = x/y = 4/7

Step-by-step explanation:

Let the fraction be x/y.

=> x + y = 2y - 3

=> x - y = -3 --------------(1)

If the numerator and denominator decrease by 1, the numerator becomes half the denominator.

=> x - 1 = 1/2(y - 1)

=> 2x - 2 = y - 1

=> 2x - y = 1 -------------(2)

Now,

On multiplying equation (1) by 2

=> 2x - 2y = -6 ------------(3)

On subtracting equation (2) - (3), we get

=> y = 7

.°. y = 7

Therefore,

x - y = -3

=> x - 7 = -3

=> x = -3 + 7

=> x = 4

.°. x = 4

Therefore, fraction = x/y = 4/7