Question

How do you solve `\frac { 5} { x } = \frac { 20} { 32}`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(32)color(blue)(x)` to eliminate the fractions while keeping the equation balanced:

`color(red)(32)color(blue)(x) xx 5/x = color(red)(32)color(blue)(x) xx 20/32`

`color(red)(32)cancel(color(blue)(x)) xx 5/color(blue)(cancel(color(black)(x))) = cancel(color(red)(32))color(blue)(x) xx 20/color(red)(cancel(color(black)(32)))`

`160 = 20x`

Now, divide each side of the equation by `color(red)(20)` to solve for `x` while keeping the equation balanced:

`160/color(red)(20) = (20x)/color(red)(20)`

`8 = (color(red)(cancel(color(black)(20)))x)/cancel(color(red)(20))`

`8 = x`

`x = 8`