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

Mar 14, 2018

$x = 4$

#### 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:

$\frac{240 + 30 x}{16 + x} = \frac{18}{1}$

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:

$240 + 30 x = \textcolor{b l u e}{18 \left(16 + x\right)}$

$= 240 + 30 x = \textcolor{b l u e}{288 + 18 x}$

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

$30 x = 48 + 18 x$

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

$12 x = 48$

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

Hope this helps!

Mar 14, 2018

$x = 4$

#### Explanation:

Start out by multiplying $16 + x$ on both sides to remove the division aspect:
$\frac{240 + 30 x}{\cancel{16 + x}} \cdot \cancel{16 + x} = 18 \cdot \left(16 + x\right)$
$240 + 30 x = 18 \left(16 + x\right)$

Now use the distributive property to simplify the right side of the equation.
$240 + 30 x = 18 \left(16 + x\right)$
$240 + 30 x = \left(18 \times 16\right) + \left(18 \times x\right)$
$240 + 30 x = 288 + 18 x$

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

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

Now divide to solve:
$\frac{\cancel{12} x}{\cancel{12}} = \frac{48}{12}$
$x = \frac{48}{12}$
$x = 4$