To represent the price of an item after tax, we can create two different expressions based on the item price $p$ and a sales tax rate of 6%.

Expression 1: Using the tax as an additional amount

The price after tax can be calculated by adding 6% of $p$ to the original price $p$.

• The sales tax is $0.06p$.
• Therefore, the total price is: $p + 0.06p = 1.06p$

Expression 2: Using a single factor

Alternatively, you can directly calculate the price after tax by multiplying the original price by $1 + 0.06 = 1.06$.

• So the price after tax is: $1.06p$

Showing the two expressions are equal:

Both expressions give the same result: $p + 0.06p = 1.06p$ Thus, the two expressions are equivalent.

Would you like further details or clarifications? Here are five related questions:

1. How would the expression change if the tax rate were 8%?
2. What is the final price if $p = 50$ dollars with a 6% tax?
3. How would you express the total price after a discount followed by tax?
4. Can you represent the price after tax as a function of $p$?
5. How would you solve for $p$ if the total price after tax is known?

Tip: When dealing with percentage increases, multiplying by $1 + \text{rate}$ is often a quicker method than adding the percentage separately.