SOLUTION: I paid $100 for an item. 12% tax was included in the price. What is the formula for finding the hidden tax on the item and the tax amount I actually paid?

Question 770283: I paid $100 for an item. 12% tax was included in the price. What is the formula for finding the hidden tax on the item and the tax amount I actually paid?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
I paid $100 for an item. 12% tax was included in the price. What is the formula for finding the hidden tax on the item and the tax amount I actually paid?
.
"Amount paid" = "cost of item" + "amount of tax"
"Amount paid" = "cost of item" + .12("cost of item")
or, factoring out "cost of item" on right:
"Amount paid" = "cost of item"(1 + .12)
"Amount paid" = (1.12)"cost of item"
.
using:
"Amount paid" = (1.12)"cost of item"
plug in what you know:
100 = (1.12)"cost of item"
100/1.12 = "cost of item"
$89.29 = "cost of item"
.
Two ways to find tax:
"amount paid" - "cost of item":
100 - 89.29
$10.71 (tax)
.
OR,
"tax rate" * "cost of item"
.12("cost of item")
.12(89.29)
$10.71 (tax)

RELATED QUESTIONS
If $1,500.00 was the total price paid for an item, including the 6% sales tax, what is... (answered by Alan3354,ewatrrr)

if you paid $22 (including tax) for an item where the tax rate is 10%, how was the price... (answered by tutorcecilia)

If you paid $44 (including tax) for an item where the tax rate is 20%, how much was the... (answered by Fombitz)

The cost of an item is given by the formula c= p+t where p is the price and t is the... (answered by Maths68)

If I paid $500 total for one item and sales tax of 7.75% has already been added on, how... (answered by rfer)

The total cash payment for an item is $79.55. If there is 7.50% sales tax included in... (answered by nerdybill)

You have an item that you bought but you lost the sales receipt. There are no price... (answered by ankor@dixie-net.com)

Suppose you pay a total of $345.53 for an item including sales tax. Assume sales tax is... (answered by mananth)

Alice paid $1130 for a Vespa. Included in the price was the 8.5% sales tax and $45 title. (answered by MathLover1)