reciprocal of a fraction

Algebra Level 2

The denominator of a fraction is 2 2 more than its numerator. If 13 13 is added to the numerator and 2 2 to the denominator, the reciprocal of the new fraction becomes 1 2 \dfrac{1}{2} . Find the original fraction. If your answer can be expressed as a b \dfrac{a}{b} , give a + b a+b .


The answer is 12.

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1 solution

Let the fraction be a b \dfrac{a}{b} , then

b = a + 2 b=a+2 (equation 1)

b + 2 a + 13 = 1 2 \dfrac{b+2}{a+13}=\dfrac{1}{2} (equation 2)

Solving the system of equations, we get a = 5 a=5 and b = 7 b=7 .

The desired answer is 5 + 7 = 12 5+7=\boxed{12}

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