Total cost = $120 + $45 + $75 = $240

Cost of Sales Tax = 8.25% ($240) = 0.0825 ($240) = $19.80

Step 1: Find the amount of tax tax paid

Jim paid \(\displaystyle \$38.88\) including tax for shoes that were \(\displaystyle \$36\) pre-tax. Therefore:

\(\displaystyle \$38.88-\$36.00=\$2.88\)

Jim paid \(\displaystyle \$2.88\) in tax.

Step 2: Figure out the tax rate (What percentage of \(\displaystyle \$36.00\) is \(\displaystyle \$2.88\)?)

Set up a proportion and solve for \(\displaystyle x\):

\(\displaystyle \frac{2.88}{36}=\frac{x}{100}\)

\(\displaystyle 288 = 36x\)

\(\displaystyle x=8\)

Therefore, Jim paid an \(\displaystyle 8\%\) tax on the shoes he purchased.

If a given locality charges \(\displaystyle 5.5\%\) sales tax, what is the total price for purchasing an item that costs \(\displaystyle \$145\)  before tax?

First, convert \(\displaystyle 5.5\%\) to \(\displaystyle 0.055\).  Then, multiply this by \(\displaystyle 145\) to get \(\displaystyle 7.975\) dollars.  Add this to the original price to get \(\displaystyle 152.975\). This rounds to \(\displaystyle \$152.98\).

Another way to do this is to multiply \(\displaystyle 145 * 1.055\) to get the same amount.

To find how much total is payed for an item after sales tax, conver the sales tax to a decimal and add it to 1, then multiply that total to the price of the item.
\(\displaystyle 8.5\%/100 = .085 \newline 1 + .085 = 1.085 \newline 1.085*23.45 = 25.44325 = \$25.44\)

You evaluate $50.00 x (0.08) = $4.00

The easiest way to do this is to write out the equation as though you were solving from the original price to find the final price. You would know that:

\(\displaystyle x+0.06x=15449.5\) or

\(\displaystyle 1.06x=15449.5\)

Solving for \(\displaystyle x\), you get:

\(\displaystyle x=14575\)

Simple interest = Amount borrowed x Interest rate =

150,000 x 6% = 150,000 x .06 = $9000

This requires us to keep track of Amy's expenses. After her first month, the unpaid balance was 500 - 80 = $420.

However, after the second month, her unpaid balance went up to $480.

5% of 480 can be obtained by multiplying

480 x .05 = 24

The simple interest formula is given by I = PRt where I = interest, P = principal, R = rate, and t = time.

Here, I = 10,000 * 0.09 * 5 = $4,500. 

The total repayment amount is the interest plus the principal, so $4,500 + $10,000 = $14,500 total repayment.

Simple interest has the formula of:

\(\displaystyle I=P*R*T\), where \(\displaystyle P\) is the starting balance, \(\displaystyle R\) is the interest rate, and \(\displaystyle T\) is the number of accrual periods.

For our data, this is simply:

\(\displaystyle 145=x*0.02*15\)

Simplifying, we get:

\(\displaystyle 0.3x=145\)

Divide both sides by \(\displaystyle 0.3\) to get:

\(\displaystyle 483.333333...\)