Question

problems 1–2: a city has a 5% sales tax.

1. a toothbrush costs $3.40 before tax. how much does it cost including tax?
2. a book costs $32.55 after tax. how much did it cost before tax?

Explanation:

Problem 1:

Step1: Understand the tax rate

The sales tax rate is 5%, which is 0.05 in decimal. The formula for the total cost including tax is \( \text{Total Cost} = \text{Before Tax Cost} \times (1 + \text{Tax Rate}) \).

Step2: Calculate the total cost

The before - tax cost of the toothbrush is $3.40. Using the formula, we substitute the values: \( \text{Total Cost}=3.40\times(1 + 0.05) \)
First, calculate \( 1+0.05 = 1.05 \). Then, \( 3.40\times1.05=3.40\times1+3.40\times0.05 = 3.40+0.17=3.57 \)

Step1: Define the formula

Let the before - tax cost be \( x \). The after - tax cost is given by the formula \( \text{After Tax Cost}=x\times(1 + \text{Tax Rate}) \). We know the tax rate is 5% or 0.05, and the after - tax cost is $32.55. So the equation is \( 32.55=x\times(1 + 0.05) \)

Step2: Solve for \( x \)

We can rewrite the equation as \( x=\frac{32.55}{1 + 0.05} \)
First, calculate \( 1 + 0.05=1.05 \). Then, \( x=\frac{32.55}{1.05}=31 \)

Answer:

The toothbrush costs $3.57 including tax.

Problem 2: