MATH SOLVE

2 months ago

Q:
# The denominator of a fraction is 5 more than twice the numerator. If both numerator and denominator are decreased by 7, the simplified result is 1/6 . Find the original fraction. (Do NOT simplify.)

Accepted Solution

A:

Answer:numerator is 10denominator is 25Step-by-step explanation:let x be the numeratorlet y be the denominatorwrite 2 equations:y = 5 + 2x[tex]\frac{x-7}{y-7}[/tex] = [tex]\frac{1}{6}[/tex]y is already isolated in the first equation, substitute into the second equation:[tex]\frac{x-7}{5+2x-7}[/tex] = [tex]\frac{1}{6}[/tex]simplify:[tex]\frac{x-7}{2x-2}[/tex] = [tex]\frac{1}{6}[/tex]cross multiply:2x - 2 = 6(x - 7)simplify:2x - 2 = 6x - 42subtract 2x:-2 = 4x - 42add 42:4x = 40divide by 4:x = 10plug in 10 for x in the first equation:y = 5 + 2(10)y = 5 + 20y = 25numerator is 10denominator is 25