Question

the denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6, find the fraction (linear equation)​

Answer 1

Step-by-step explanation:

Let the numerator be x

And the denominator be y

Case 1:-

Denominator = 2(Numerator) + 4

⇢y = 2x + 4

⇢2x - y = -4.....(i)

Case 2:-

⇢(Denominator - 6 ) = 12(Numerator - 6)

⇢ y - 6 = 12(x - 6)

⇢y - 6 = 12x - 72

⇢12x - y = 72 - 6

⇢12x - y = 66......(ii)

Subtracting equation (i) from (ii)

⇢12x - y - (2x - y) = 66 - (-4)

⇢12x - y - 2x + y = 66 +4

⇢10x = 70

⇢x = $\dfrac{70}{10} = 7$

Substitute x = 7 in equation (i)

⇢2x - y = -4

⇢2(7) - y = -4

⇢14 - y = -4

⇢-y = -4 - 14 = -18

⇢y = 18

The numerator = x = 7

The denominator = y = 18

$\dashrightarrow\underline{\boxed{\rm \therefore The \: fraction =\frac{7}{18}}}$