Question

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

Step-by-step explanation:

Let the numerator be x and denominator be y.

Let the fraction be x/y

x+y+3=2y

(or) x−y=−3

(or) x=y−3 _____ (1)

Also , x-1 / x-1 = 2

x-1 = y-1 /2

(or) 2x−y=1 _____ (2)

substituting (1) in (2),

2(y−3)−y=1

⇒2y−6−y=1⇒y=7

put y=7 in (1) we get x=7−3=4

∴x=4,y=7

∴ the fraction is x / y = 4 / 7

Answer 2

Answer:-

• The fraction is 4/7

Step by Step Explaination:-

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

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

x - 1 = $\frac{1}{2}$ (y - 1)

→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;

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