Question

How do you solve `\frac{27}{x}=\frac{81}{45}`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(blue)(45)color(red)(x)` to eliminate the fraction and isolate the `x` term while keeping the equation balanced. `45x` is the lowest common denominator of the two fractions:

`color(blue)(45)cancel(color(red)(x)) xx 27/color(red)(cancel(color(black)(x))) = cancel(color(blue)(45))color(red)(x) xx 81/color(blue)(cancel(color(black)(45)))`

`1215 = 81x`

Now, divide each side of the equation by `color(red)(81)` to solve for `x` while keeping the equations balanced:

`1215/color(red)(81) = (81x)/color(red)(81)`

`15 = (color(red)(cancel(color(black)(81)))x)/cancel(color(red)(81))`

`15 = x`

`x = 15`