Question

The denominator of a fractions is 4 more than twice the numerator. When both numerator anddenominator are decreased by 6, then the denominator becomes 12 times the numerator. Findthe fraction​

Answer 1

Answer:

7/18

Explanation:

We've been given a fraction who's values we're unaware of, so let us consider that;

• x ➝ Numerator

• y ➝ Denominator

Therefore, the fraction becomes x/y.

According to the question, the denominator of a fraction is 4 more than twice the numerator, therefore;

$\sf \dashrightarrow Denominator = 4 + 2(Numerator)$

$\sf \dashrightarrow y = 4 + 2x$

$\sf \dashrightarrow \textsf{\textbf{2x - y = -4}} \ \ \ \dots Equation(1)$

Also according to the question, when both numerator and denominator are decreased by 6, the denominator becomes 12 times the numerator. Therefore;

Numerator ➝ x - 6

Denominator ➝ y - 6

$\sf \dashrightarrow Denominator = 12(Numerator)$

$\sf \dashrightarrow y - 6 = 12(x - 6)$

$\sf \dashrightarrow y - 6 = (12)x - (12)6$

$\sf \dashrightarrow y - 6 = 12x - 72$

$\sf \dashrightarrow - 6 + 72 = 12x - y$

$\sf \dashrightarrow 66 = 12x - y$

$\sf \dashrightarrow \textsf{\textbf{12x - y = 66}} \ \ \ \dots \ Equation(2)$

On subtracting Equation (2) from Equation (1) we get;

$\sf \dashrightarrow (2x - y) - (12x - y) = -4 - 66$

$\sf \dashrightarrow 2x - y - 12x + y = -70$

$\sf \dashrightarrow 2x - 12x - y + y = -70$

$\sf \dashrightarrow - 10x = -70$

$\sf \dashrightarrow x = \dfrac{-70}{-10}$

$\sf \dashrightarrow \textsf{\textbf{x = 7}}$

We've got the value of the numerator, we'll substitute x's value in Equation (1) to find the value of the denominator.

$\sf \dashrightarrow 2x - y = -4$

$\sf \dashrightarrow 2(7) - y = -4$

$\sf \dashrightarrow 14 - y = -4$

$\sf \dashrightarrow 14 + 4 = y$

$\sf \dashrightarrow \textsf{\textbf{18 = y}}$

Therefore;

x = 7, and y = 18, which makes the fraction 7/18.

Answer 2

Answer:

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