How do you 'back out' sales tax?

Feb. 25, 2005 — Q: How do you “back out” sales tax? On a $20,000.00  purchase (total with tax) and a sales tax of 7 percent,  how much do I send to the state? — Ruth, Tinley Park, Ill.

A: Don’t you hate these? It’s like one of those annoying questions on a standardized test. But here goes:

In this case, you need to figure out how much of that $20,000 purchase (let’s call it a car) went for the car and how much is tax. So let’s do the math:

• Step one: Set up the problem
      Car + Tax (7 percent of Car) = $20,000  
• Step two: Solve for "Car"
      (1) * Car + (.07) * Car = $20,000  
• Step three: Add up the pieces
      1.07 * Car = $20,000
• Step four: Divide both sides by 1.07
      Car = $20,000 / 1.07
• Step five: Voila!
      Car = $18,691.59
  
  

So you “back out” the tax by subtracting the price of the car from the total $20,000 you paid, you get: $20,000 - $18, 691.59 = $1,308.41

To double check, you can see what the tax is by taking 7 percent of the cost of the car alone, or $18,691.59.

• Tax = $18,691.59 * .07  = $1,308.41

And even if the dealer calculates it for you, it never hurts to check the math.