# Tutor couldnt explain?

You paid \$26696.5 for a new car. This includes the 7% sales tax. What was the original cost of the car?

So i got help from a tutor but she couldn't explain how she got it

Relevance
• The original cost of the car will be 100%.

Thus we are told 107% = \$26696.5

Therefore 1% = \$26696.5 / 107

and 100% = (26696.5 / 107) x 100

• The equation for total price is:

price + price * tax rate = total

With your numbers (remember 7% = 7 / 100 = 0.07):

price + price * 0.07 = \$26696.50

price * (1 + 0.07) = \$26696.50

price * 1.07 = \$26696.50

price = \$26696.50 / 1.07

price = \$24950.00

So the original price is \$24950.00.

You can double check your work with a sales tax calculator like: http://www.sale-tax.com/Calculator?price=24950.00&...

• The car cost \$26696.5 including 75 sales tax

In equation form this looks like:

26696.5 = x + 0.07x

This is because you are adding the original cost of the car (x) as well as 7% of the original cost to get \$26696.5.

Now solve for the equation:

26696.5 = 1.07x

x = 26696.5/1.07

I'll let you solve for that, hope this helps!

• c = original price of car

tax = 7% of c = 0.07c

total cost = c + 0.07c = c(1 + 0.07) = 1.07c

1.07c = 26696.5

c = 26696.5/1.07 = [fill in]