In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and denominator the new fraction is $\frac{2}{3}$. Find the original fractions.

Given:

In a fraction, twice the numerator is 2 more than the denominator

 is added to  numerator and denominator the new fraction is $\frac{2}{3}$

To do: Find the original fractions

Solution:

Let the fraction by $\frac{x}{y}$

$ 2x = y + 2$; or$ y = 2x - 2$

and $\frac{x+3}{y+3} = \frac{2}{3}$

Substituting $\frac{x+3}{2x-2 + 3} = \frac{x+3}{2x+1} = \frac{2}{3}$

Solving $3(x+3) = 2(2x+1) \ or \ 3x + 9 = 4x + 2  or 4x - 3x = x = 9 - 2 = 7$

So $y = 2x - 2 = 2(7) - 2 = 14 - 2 = 12$

So the fraction is $\frac{x}{y}$ or $\frac{7}{12}$

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Updated on: 10-Oct-2022

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