The Denominator Of A Fraction Is Greater Than Its Numerator By 12. If The Numerator Is Decreased By 2 And The Denominator Is Increased By 7, The New F

The denominator of a fraction is greater than its numerator by 12. If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction is equivalent with one upon two. Find the fraction.

Answer: 23/35

Solution:

Let x be the numerator

and x + 12 be the denominator

 \frac{(x) - 2}{(x + 12) + 7}  =  \frac{1}{2}  \\  \frac{x - 2}{x + 19}  =  \frac{1}{2}  \\ 2x - 4 = x + 19 \\ x = 23

Check:

  \frac{x - 2}{x + 19}  =  \frac{1}{2}  \\  \frac{23 - 2}{23 + 19}  =  \frac{1}{2}  \\  \frac{21}{42}  =  \frac{1}{2}  \\  \frac{1}{2}  =  \frac{1}{2}

^_^


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