Question

arthur wants to buy an item that costs p dollars before tax. using a 6% sales tax rate, write two different expressions that represent the price of the item after tax show that the two expressions are equal

Answer 1

For this case we have the following variable:

p: cost of the item that Arthur wants to buy before tax

The expression for the 6% tax is given by:

$\frac{6}{100} p$

Or equivalently:

$0.06p$

Therefore, two different expressions for the total cost are:

Expression 1:

$p + \frac{6}{100} p$

Expression 2:

$p + 0.06p$

To prove that they are equal, suppose that the item costs $ 100:

Expression 1:

$p + \frac{6}{100} p$

$100+ \frac{6}{100} 100$

$100 + 6$

$106$

Expression 2:

$p + 0.06p$

$100 + 0.06 (100)$

$100 + 6$

$106$

Since the cost is the same, then the expressions are the same.

Answer:

Two different expressions that model the problem are:

$p + \frac{6}{100} p$

$p + 0.06p$