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
[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 - 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
