Question

The Sanchez family had dinner at their favorite restaurant. A 9% salestax was added to their bill. Amy paid the bill with a $10 gift certificateplus $30.60. How much did the family's dinner cost before tax? Roundyour answer to the nearest penny.Hint: Use the equation P+rP=T,where P is the price before tax, r is the sales tax rate, and T is the totalprice, including tax.

Answer 1

The formula indicates how the price of the meal after taxes is calculated.

`T=P+rP`

Where

T is the total price

P is the price without taxes

r is the tax rate, this value is always expressed as a decimal value.

Amy paid a total of $30.60 plus a $10 gift certificate, the total cost of the bill is:

`\begin{gathered} T=30.6+10 \\ T=40.6 \end{gathered}`

To express the tax rate as a decimal value you have to divide the percentage by 100:

`\begin{gathered} r=(9)/(100) \\ r=0.09 \end{gathered}`

Replace both values on the formula:

`P+0.09P=40.60`

Now we have established an equation with one unknown "P", to solve the equation for P, the first step is to simplify both terms on the left side of the equation. To do so, add both terms:

`\begin{gathered} P+0.09P=40.60 \\ 1.09P=40.60 \end{gathered}`

Divide both sides by 1.09 to determine the value of P

`\begin{gathered} (1.09P)/(1.09)=(40.60)/(1.09) \\ P=37.249\approx37.25 \end{gathered}`

The cost of the family's dinner before taxes w