Samuel paid $9.10, including tax, for a dog collar. Before tax, the original price of the collar was $8.75. What was the sales tax rate?

Question

Let r represent the rate as a decimal. Complete the equation that represents the problem. (Hint: The original price of the collar plus the amount of tax equals the total cost including tax.)

Answer 1

To compute the sales tax rate, we start with the information given in the problem:

• Let \( P \) be the original price of the collar, which is \( P = 8.75 \).
• Let \( r \) be the sales tax rate expressed as a decimal.
• The total price including tax is \( 9.10 \).

The relationship between the original price, tax, and total price can be expressed as:

\[ \text{Total Price} = \text{Original Price} + \text{Tax} \]

The tax can be calculated as the original price multiplied by the sales tax rate. Thus, we can write the equation as:

\[ 9.10 = 8.75 + (8.75 \cdot r) \]

This is the complete equation that represents the problem.

Answer 2

What is the sales tax rate?

Answer 3

To find the sales tax rate \( r \), we can start with the equation we set up:

\[ 9.10 = 8.75 + (8.75 \cdot r) \]

Next, we will isolate \( r \).

1. Subtract \( 8.75 \) from both sides:

\[ 9.10 - 8.75 = 8.75 \cdot r \]

Calculating the left side:

\[ 0.35 = 8.75 \cdot r \]

2. Now, divide both sides by \( 8.75 \) to solve for \( r \):

\[ r = \frac{0.35}{8.75} \]

3. Calculate \( r \):

\[ r = 0.04 \]

So, the sales tax rate as a decimal is \( 0.04 \). To express it as a percentage, you can multiply by 100:

\[ r = 0.04 \times 100 = 4% \]

Thus, the sales tax rate is 4%.