Question

How do you solve `30/42 = 55/x`?

Answer 1

See a solution process below

Explanation:

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

`42/30 = x/55`

Now, we can multiply each side of the equation by `color(red)(55)` to solve for `x` while keeping the equation balanced:

`color(red)(55) xx 42/30 = color(red)(55) xx x/55`

`color(red)((5 xx 11)) xx (7 xx 6)/(5 xx 6) = cancel(color(red)(55)) xx x/color(red)(cancel(color(black)(55)))`

`color(red)((color(black)(cancel(color(red)(5))) xx 11)) xx (7 xx color(blue)(cancel(color(black)(6))))/(color(red)(cancel(color(black)(5))) xx color(blue)(cancel(color(black)(6)))) = x`

`color(red)(11) xx 7 = x`

`77 = x`

`x = 77`

Answer 2

#x = 77

Explanation:

What we do to one side, we must do to the other...

First thing to do is to multiply both sides by `x`

`=> 30/42 xx x = 55/x xx x`

We can cancel out the `x` on the right side, as it is on the numerator and denominator

`=> 30/42x = (55cancel(x))/cancel(x)`

`=> 30/42x = 55`

Now we need to isolate the `x`, so divide each side by `30/42`

`=> (30/42x)/(30/42) = 55/(30/42)`

`=> (cancel(30/42)x)/(cancel(30/42)) = 55/(30/42)`

When we use a calculator we see that `55/(30/42) = 77`

`=> x = 77`