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

2 Answers
Mar 14, 2018

Answer:

#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

Answer:

#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#