Question

How do you solve `50w \div ( 90+ w ) = 20`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(50w)/(90 + w) = 20`

Next, multiply each side of the equation by `color(red)((90 + w))` to eliminate the fraction while keeping the equation balanced:

`color(red)((90 + w)) xx (50w)/(90 + w) = color(red)((90 + w)) xx 20`

`cancel(color(red)((90 + w))) xx (50w)/color(red)(cancel(color(black)(90 + w))) = color(red)(90 xx 20) + (w xx 20)`

`50w = 1800 + 20w`

Then, subtract `color(red)(20w)` from each side of the equation to isolate the `w` term while keeping the equation balanced:

`50w - color(red)(20w) = 1800 + 20w - color(red)(20w)`

`(50 - color(red)(20))w = 1800 + 0`

`30w = 1800`

Now, divide each side of the equation by `color(red)(30)` to solve for `w` while keeping the equation balanced:

`(30w)/color(red)(30) = 1800/color(red)(30)`

`(color(red)(cancel(color(black)(30)))w)/cancel(color(red)(30)) = 60`

`w = 60`