Question

13. The sum of denominator
and numerator of a fraction is
3 less than twice the
denominator. If each of the
numerator and denominator is
denominator is decreased by
1, the fraction becomes 1/2.
Find the fraction.​

Answer 1

Answer:

Fraction is 4/7

Step-by-step explanation:

Let the numerator be x and denominator be y

x + y = 2y - 3

x + y - 2y = -3

x - y = -3

x = -3 + y.....(1)

x - 1 / y - 1 = 1 / 2

2 ( x - 1 ) = y - 1

2x - 2 = y - 1

2x - y = -1 + 2

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

Substituting (1) in (2)

2( - 3 + y ) - y = 1

-6 + 2y - y = 1

y = 1 + 6

y = 7

Substituting y = 7 in (2)

2x - (7) = 1

2x  = 1 + 7

2x = 8

x = 4

Answer 2

⭕The given problem is on linear equations with two variables say x and y.

⭕Let the fraction required be x/y.

⭕Sum of numerator and denominator = x + y

⭕Given x + y is 3 less than twice the denominator

$→ x + y = 2y - 3$

$</p><p>x - y +3 = 0 → (1)$

⭕Also, if numerator and denominator are decreased by 1

$→ (x - 1), (y - 1)$

⭕The numerator becomes half of the denominator

$2x - 2 = y – 1$

$2x - y =2 -1 =1$

$2x - y = 1 → (2)$

⭕Subtracting (2) and (1) gives

$x - y + 3 - (2x - y - 1) = 0$

$x - y + 3 – 2x + y + 1 = 0$

$-x + 4 =0$

$x = 4$

⭕Substituting x value in (1) gives

$4 - y + 3 = 0$

$y = 7$

⭕Therefore x = 4 and y = 7;

⭕The fraction required is. $\frac{4}{7}$

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