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

Question

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 $10.6$.