Question

How do you solve `(240+30x)/(16+x)=18`?

Answer 1

`x=4`

Explanation:

We can get rid of the denominator by multiplying it by `18`. Here, we are essentially cross-multiplying:

Let's say the problem is:

`(240+30x)/(16+x)=18/1`

Since the numerator of the first term will be unaffected (multiplied by `1`), we would only multiply `18` and `16+x`. Our new equation is:

`240+30x=color(blue)(18(16+x))`

`=240+30x=color(blue)(288+18x)`

We can subtract `240` from both sides to get:

`30x=48+18x`

Next, we can subtract `18x` from both sides to get:

`12x=48`

And finally, dividing both sides by `12` will get us to `x=4`.

Hope this helps!

Answer 2

`x = 4`

Explanation:

Start out by multiplying `16 + x` on both sides to remove the division aspect:
`(240+30x)/cancel(16+x) * cancel(16 + x)=18 * (16 + x)`
`240 + 30x = 18(16 + x)`

Now use the distributive property to simplify the right side of the equation.
`240 + 30x = 18(16 + x)`
`240 + 30x = (18 xx16) + (18 xx x)`
`240 + 30x = 288 + 18x`

Now subtract `240` from both sides to simplify:
`240 + 30x = 288 + 18x`
`30x = 48 + 18x`

Once last subtraction! Subtract `18x` from both sides:
`30x = 48 + 18x`
`12x = 48`

Now divide to solve:
`(cancel12x)/cancel12 = 48/12`
`x = 48/12`
`x = 4`