Question

A store charges 6% sales tax. The total cost of an item with price p is p+0.06p. What is an equivalent expression?
p = 10
p + 0.06p
10 + 0.06 (10)
10 + _
10.6

1.06p
1.06 (_)
_

So, the expressions are _.

Answer 1

To evaluate the expressions involving the sales tax, let's break it down step by step:

1. The total cost of an item with price \( p \) including a 6% sales tax can be represented as:
\[
\text{Total Cost} = p + 0.06p
\]

2. This can be factored:
\[
\text{Total Cost} = p(1 + 0.06) = p(1.06)
\]

3. Therefore, an equivalent expression for the total cost, incorporating the sales tax, is:
\[
1.06p
\]

Now let's plug in \( p = 10 \):

4. Calculate the total cost with \( p = 10 \):
\[
\text{Total Cost} = 10 + 0.06(10) = 10 + 0.6 = 10.6
\]
This confirms that when \( p = 10 \), the total cost is indeed \( 10.6 \).

So, in summary:
- The expressions are \( 1.06p \) and for \( p = 10 \), it becomes \( 10.6 \).

Thus, we can say:
- The expressions are \( 1.06p \) and \( 10.6 \).