Question

A fraction equals 8/9. The numerator is 2 more than 6 times the quotient of the denominator and 7. Find the reciprocal of the original fraction

Answer 1

@jim_thompson5910

Answer 2

So this is my set up. 6(x+7)=8/9 or is it 6(x+7)/x=8/9?

Answer 3

`A fraction equals 8/9`

so we have 2 numbers x and y divide like this x/y and they will reduce to 8/9

so that means x/y = 8/9

agreed?

Answer 4

Yup but could we approach this with 1 variable?

Answer 5

yes, but it helps to start off with 2 variables then do a substitution

Answer 6

x = numerator
y = denominator

`The numerator is 2 more than 6 times the quotient of the denominator and 7`
so
(numerator) = 6*(denominator/7) + 2
x = 6*(y/7) + 2

agreed?

Answer 7

agree!

Answer 8

so we go from
\[\Large \frac{x}{y} = \frac{8}{9}\]
to
\[\Large \frac{6(y/7)+2}{y} = \frac{8}{9}\]

Answer 9

Alrighty! Thank you

Answer 10

I got confused with the wording of the equation :)

Answer 11

you're welcome