A television set has been marked up 250% and is being sold $315. What was the original price of the television set?

In this problem, there is an unknown number: the original price of the television before it was marked up 250%.

If we recall, whenever there is an unknown number in a problem, you may replace the unknown number with a variable. In this problem, we will use the letter #p# to represent the word "price".

Now that we have established our unknown number and what it represents, let's model the equation being described by using this variable.

Here is what the equation should look like:

#p + 250% * p = 315#

As we already established, #p# represents the original price. But what does #250% * p# represent? #250% * p# represents how much money the television is being marked up. And #315# is the price at which the television is being sold for.

So now that we have our equation, let's get to work solving it.

First of all, whenever there's a variable just by itself, you can always multiply it by #1# and the result would still be that same number. Using that information, we can multiply the #p# at the front of the equation by #1# like so:

#1p + 250% * p = 315#

The second thing we need to remember is that #1# can be any fraction as long as both its numerator and denominator are the same because any number divided by itself would be #1#. Now, let's convert #250%# to #250/100#, turn #1# to #100/100#, and rewrite the equation:

#100/100p + 250/100 * p = 315#

And that simplifies to:

#350/100p = 315#

Next, we can turn #350/100# to #3.5#. So now, the equation is:

#3.5p = 315#

Finally, we can use the Division Property of Equality to divide 3.5 on both sides, which results in the answer:

#p = 90#