Question

The sum of the numerator and
denominator of a fraction is 4 more than
twice the numerator. If the numerator
and denominator are increased by 3,
they are in the ratio 2:3. Determine the
fraction.​

Answer 1

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Answer 2

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Pair of Linear Equations in Two Variables

Algebraic Solution of a Pair of Linear Equations

The sum of the numerator an...

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The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2:3. Determine the fraction

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ANSWER

Let numerator =x and denominator=y

∴Fraction=

y

x

According to the first condition

⇒x+y=2x+4

⇒y=x+4.....eq1

According to the second condition

⇒

y+3

x+3

=

3

2

⇒3x+9=2y+6⇒3x−2y=−3....eq2

Substitute the value of y from eq1 to eq2

⇒3x−2(x+4)=−3⇒3x−2x+8=−3⇒x=5

Put x=5 in eq1

⇒y=5+4⇒y=9

Hence,fraction=

9

5

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