Find the cost of the stereo before tax.

Question

Including a 6% sales tax, a new stereo costs $429.3. Find the cost of the stereo before tax.

A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation. (1)

The equation is

B) Solve your equation in part [A] to find the original price of the stereo.

Answer: The original price of the stereo before tax was dollars.

Answer 1

It helps to think about what you would have to do to a number to find the number plus tax. The price of the stereo is the unknown variable (x).

x(1+r)=P Where r is the tax rate and P is the price of the item after tax.

x(1+.06)=429.30 Equation filled in

x(1.06)=429.30 Add the 1 and the tax rate

1.06x=429.30 Simplified

1.06x/1.06=429.30/1.06 Divide both sides by 1.06 to single out the variable

x=405 Variable discovered.

That is the complicated algebra fashion if you need it drawn out. Now to make it logically more simple just divide the end price by the (tax rate plus 1). 

429.30/1.06 it will work every time.

  

Answer 2

A.  Since the tax rate is 6%, the decimal equivalent it .06.

By multiplying the original price of the stereo, x, by 1 + the sales tax, you get the cost after tax.

(1 + .06)x = 429.30

1.06x = 429.30

B.  x = 429.30/1.06

x = $405