Real World or Naw: A Praxis Problem

 

The following problem is a type of problem my preservice teachers encounter on the Praxis II Multiple Mathematics assessment:


 If the price of a computer, including a 9% tax, is $3,545.00, what is the cost of the computer before the tax is added?


Traditionally, students are asked to find the cost of an item after adding tax to the original cost. Moreover, students are asked to find the total cost of an item after applying some sort of discount. The above problem is like a reverse operation or is it. 

Let's review how to compute sale tax and the cost of something after adding the sale tax.

Let's say a computer costs $1575 without the tax included. There is an 8% tax to add to the cost of the computer. $1575 X .08= $126. Then, add the $126 to the cost of the $1575 + $126=$1701. The computer will cost $1701. This does not include the warranty or service plan. 

The math is straightforward computation, and the situation is real world. What Praxis wants to know is if you can calculate the original cost when provided the tax in percent and the final amount.

The challenge with this type of problem is there is no original cost given to calculate the tax cost. Therefore, you will have to think about ways of finding the cost of something with the tax.

Since we do not know the cost, we will need to establish a variable to represent it. N will stand for the original cost. To find the tax, we must remember what we do to the original cost. We multiply it by the tax. In this case, it is 9%. Then we add that amount to the original cost. So in essence (100% +9%)N= price including sales tax.

That is (100% + 9%)N=$3545. We usually convert percent to decimal, therefore, (1.00 + .09)N=$3545.

1.09N=$3545. If you simply remember algebra, you divide each side by 1.09. The original cost will be $3252.30

This makes much sense being that you must add the tax to the original cost but to find the tax you multiply the tax in percent by the original cost.

Leave a comment about this kind of problem. Why would we need to find the original cost of something? Why is this important for students to know?

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