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.

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.

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.

Learn how to calculate the price of an item after applying a 6% sales tax with two different expressions. Understand how both expressions yield the same result using algebraic principles. Suitable for students in Grades 6-8.

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