Question

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.)

Answer 1

Answer:

numerator is 10

denominator is 25

Step-by-step explanation:

let x be the numerator

let y be the denominator

write 2 equations:

y = 5 + 2x

$\frac{x-7}{y-7}$ = $\frac{1}{6}$

y is already isolated in the first equation, substitute into the second equation:

$\frac{x-7}{5+2x-7}$ = $\frac{1}{6}$

simplify:

$\frac{x-7}{2x-2}$ = $\frac{1}{6}$

cross multiply:

2x - 2 = 6(x - 7)

simplify:

2x - 2 = 6x - 42

subtract 2x:

-2 = 4x - 42

add 42:

4x = 40

divide by 4:

x = 10

plug in 10 for x in the first equation:

y = 5 + 2(10)

y = 5 + 20

y = 25

numerator is 10

denominator is 25