Question: A group of friends buys 15 movie tickets for a total of $147.66, which includes a 7% sales tax.
Before tax, how much did a single movie ticket cost?
1. **State the problem:** We need to find the price of a single movie ticket before tax, given that 15 tickets cost $147.66 including a 7% sales tax.
2. **Identify the formula:** The total cost including tax is given by $$\text{Total Cost} = \text{Price before tax} \times (1 + \text{Tax Rate})$$
3. **Define variables:** Let $p$ be the price of one ticket before tax.
4. **Calculate total price before tax:** Since 15 tickets were bought, the total price before tax is $$15 \times p$$.
5. **Set up the equation:** Including 7% tax, the total cost is
$$15p \times 1.07 = 147.66$$
6. **Solve for $p$:**
$$15p = \frac{147.66}{1.07}$$
$$15p = 138.00$$
7. **Divide both sides by 15:**
$$p = \frac{138.00}{15}$$
$$p = \cancel{\frac{138.00}{\cancel{15}}} \approx 9.20$$
8. **Interpretation:** The price of a single movie ticket before tax is approximately $9.20.