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

2 Answers
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:

(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!

Mar 14, 2018

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