A local service technician charges $149.80 for a service call. This price includes a 7% sales tax. How much of the charge is sales tax? Round to the nearest hundredth.

Steps to Solve

1. Define the variables

Let $x$ be the price of the service before tax. The total charge is $149.80, which includes a 7% sales tax.

2. Set up the equation

The total charge is the price before tax plus the sales tax, which is 7% of the price before tax. Therefore, we have the equation: $x + 0.07x = 149.80$

3. Solve for x

Combine the terms with $x$: $1.07x = 149.80$

Divide both sides by 1.07: $x = \frac{149.80}{1.07}$ $x \approx 140$

4. Calculate the sales tax

The sales tax is 7% of the price before tax, which is $x$. Sales tax $= 0.07x$ Sales tax $= 0.07 \times 140$ Sales tax $= 9.8$

5. Alternative approach: Directly calculate the sales tax

Let $T$ be the total charge ($149.80), and let $r$ be the sales tax rate (7% or 0.07). Let $S$ be the sales tax amount. Then $T = x + rx$, which means $T = x(1+r)$. We want to find the sales tax amount $S = rx$. From $T = x(1+r)$, we have $x = \frac{T}{1+r}$. Substitute this into $S = rx$ to get $S = r \cdot \frac{T}{1+r} = \frac{rT}{1+r}$. $S = \frac{0.07 \times 149.80}{1 + 0.07} = \frac{0.07 \times 149.80}{1.07} = \frac{10.486}{1.07} \approx 9.80$