Question

1. Form a pair of linear equations for: The sum of the numerator and denominator of

fraction is3 less than twice the denominator. If the numerator and denominator both are

decreased by 1, the numerator becomes half the denominator.​

Answer 1

The fraction is 4/7

Step-by-step explanation:

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)x−1=

2

1

(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;

The fraction required is 4/7