Finding Percents (Sales Tax)

The last section of this unit is dealing with finding percents.  Since we are familiar with decimals and fractions (ratios included) we can use that knowledge to find percent.  In order to find sales tax, we came up with a number sentence, or formula to help us out.

Total Cost = Price + Tax, where Tax = Tax Rate X Price.

We will abbreviate this to be

C = P + T, where T = % X P

Let's take a common item, like an Xbox One.  The price for an Xbox One is $349.  The tax is Conway (rounded up) is 9%.  Since I cannot multiply by a %, I have to change that to a decimal.  So we have to do that first.  Since all percent is out of a hundred, we can write our percent as

   9    = 0.09 as a decimal.  Here is how to work the problem:
100

Alternatively, we can look at the cost of an item as having to pay

100% + 9% which would be 109%.  This would be 1.09 as a decimal.  So...

C = $349 X 1.09 = $380.41.  Either way is fine.

But what if we know how much the tax was but forgot the price?

Let's say that our tax rate is 6% and we paid $4.80.   We can use a percent bar and ratios to figure this out.

This percent bar shows what our 6% is, but not our 100%.  We can use the ratios shown above.  Since all percent is "out of 100" we can use 100 as a denominator and use what we know about equivalent ratios or fractions to get to 100%

We can also divide.  We can use what we know fact families.  Since

Tax = % (as a decimal) X price

Tax ÷ % (as a decimal) = price

$4.80 ÷ 0.06 = price

              $80 = price