1. **Problem Statement:** A customer inside the city had a $112.82 water bill (excluding sewer). To the nearest gallon, how much water did he use during the month? Use Table 11.4 for rates. 2. **Understanding the Rates:** - Inside city water rate: $15.48 for first 4000 gallons or less. - Excess water cost: $1.72 per 1000 gallons. 3. **Set up the equation:** Let $x$ = total gallons used. If $x \leq 4000$, bill = $15.48$ (which is less than $112.82$, so $x > 4000$). For $x > 4000$, bill = $15.48 + 1.72 \times \frac{x - 4000}{1000}$. 4. **Solve for $x$:** $$ 112.82 = 15.48 + 1.72 \times \frac{x - 4000}{1000} $$ Subtract 15.48 from both sides: $$ 112.82 - 15.48 = 1.72 \times \frac{x - 4000}{1000} $$ $$ 97.34 = 1.72 \times \frac{x - 4000}{1000} $$ Divide both sides by 1.72: $$ \frac{97.34}{\cancel{1.72}} = \cancel{1.72} \times \frac{x - 4000}{1000} \div \cancel{1.72} $$ $$ 56.6 = \frac{x - 4000}{1000} $$ Multiply both sides by 1000: $$ 56.6 \times 1000 = x - 4000 $$ $$ 56600 = x - 4000 $$ Add 4000 to both sides: $$ x = 56600 + 4000 = 60600 $$ 5. **Final answer:** The customer used approximately **60600 gallons** of water during the month.