Your Algebra Teacher Was Right :(

Who knew that grumpy lady was right?  The one you used to make fun of.  The one you drew less than complimentary pictures of.  When your Algebra teach would say “You’re going to need this stuff later in life” you’d mumble to your buddy in the seat next to you “Get over yourself.”  Well, time to eat some crow, my friend.  Because she was right.

Case in point: Sales Tax Calculation when “Tax is Included”

It’s always convenient to sell products in round, easy to hand-over, currency denominations, right?  Of course.  Asking a customer to fork over a five, ten, or twenty dollar bill makes life a lot easier for everyone.  But how do you calculate the sales tax when “it’s included?”

After thinking through it for a minute, I figured it out.  I was impressed that I’d actually remembered.  And I was humbled by the fact that Miss Jacobson actually taught me something when I gave her nothing but flack.  Working through the problem on my white board helped:

Known variables: Total of Sale (example $20); Tax Rate (example 9.25%)
Unknown variable (x): Product or Service Price before Tax

Equation and Work:
Step 1: x + .0925x = $20
Step 2: x (1 + .0925) = $20
Step 3: x = $20/(1 + .0925)
Step 4: x = $20/1.0925 = $18.31
Step 5: Tax = $18.31 * .0925 = $1.69

So it looks like she was right after all.  I am going to need some of what I learned in school.