Question

How do you solve `\frac{2400}{100}=\frac{180}{x}`?

Answer 1

See a couple of solution processed below:

Explanation:

Because both sides of the equation are pure fractions we can flip the fractions giving:

`100/2400 = x/180`

Next, we can reduce the fraction on the left side of the equation:

`1/24 = x/180`

Now, we can multiply each side of the equation by `color(red)(180)` to solve for `x` while keeping the equation balanced:

`color(red)(180) xx 1/24 = color(red)(180) xx x/180`

`color(red)((12 xx 15)) xx 1/((12 xx 2)) = cancel(color(red)(180)) xx x/color(red)(cancel(color(black)(180)))`

`color(red)((color(black)(cancel(color(black)(12))) xx 15)) xx 1/((color(red)(cancel(color(black)(12))) xx 2)) = x`

`15/2 = x`

`x = 15/2`

Another process would be to first reduce the fraction on the left side of the equation:

`24/1 = 180/x`

`24 = 180/x`

Now, multiply each side of the equation by `color(red)(x)/color(blue)(24)` to solve for `x` while keeping the equation balanced:

`color(red)(x)/color(blue)(24) xx 24 = color(red)(x)/color(blue)(24) xx 180/x`

`color(red)(x)/cancel(color(blue)(24)) xx color(blue)(cancel(color(black)(24))) = cancel(color(red)(x))/(color(blue)(12 xx 2)) xx (12 xx 15)/color(red)(cancel(color(black)(x)))`

`x = 1/(color(blue)(color(black)(cancel(color(blue)(12))) xx 2)) xx (color(blue)(cancel(color(black)(12))) xx 15)/1`

`x = 15/2`