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Applied Linear Equations: Tax Problem - Problem 1

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

So, here is a linear equation problem, dealing again with a tax rate. Your parents buy you a new computer for your birthday. They spend $2000, including a 5% tax rate, how much did your computer retail for?

So, in this case, tax has already been included, tax is typically an additional fee, here, we're saying that the $2000, already includes that additional fee. For any tax problem, I always go to the example, original plus tax is equal to total. We know that our total is $2000, that's given, so we know our total is 2000, what we don't know is, how much this computer actually costs. When you don't know what something is, assign it a variable typically x.

So our original price is x, if x was say 100, we're paying 5% tax on that, so it's just 5% of 100, $5, we don't know what our rate is or the amount is but we're still taking 5% of that, so our tax rate is actually 5% of that unknown and then let's add to our original to get our total.

From here it's a pretty straight forward linear equation x plus 105x is just 1.5x is equal to 2000, divide by 1.05 to finish it up and using our calculator we get 1904, 76, it's asking for the original price which is what x is, that is our answer.

I do want bring a little red flag to your attention. A common mistake people what to do is take 5% of this, 5% of 2000 and just subtract that. The tax rate on $2000 is going to be more than the tax rate on 1900, that makes sense? Because the tax is a percentage so you're going to actually get charged more tax on this than this.

So make sure you go through this process because if you just take 5% of this, you're actually going to end up with a number less than what you should, just a little red flag. Other than that as long as you use this rubric, you should be fine.

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