Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? If a person who works 40 hours per week earns \( \$ 69,800 \) per year, estimate that person's hourly wage by rounding the annual income to the nearest ten thousand. Use the estimate that there are 50 weeks in a year. The estimate of that person's hourly wage is approximately \( \$ \square \). (Round to the nearest dollar as needed.)

To estimate and calculate the person's hourly wage, follow these steps: ### **1. Estimation Without a Calculator** **Given:** - **Annual Income:** \$69,800 - **Rounding:** Nearest ten thousand → \$70,000 - **Weeks per Year:** 50 - **Hours per Week:** 40 **Steps:** 1. **Estimate Annual Income:** Rounded to the nearest ten thousand, \$69,800 becomes \$70,000. 2. **Calculate Total Annual Hours:** \[ 50 \text{ weeks/year} \times 40 \text{ hours/week} = 2,000 \text{ hours/year} \] 3. **Estimate Hourly Wage:** \[ \frac{\$70,000}{2,000 \text{ hours}} = \$35 \text{ per hour} \] **Estimated Hourly Wage:** **\$35** --- ### **2. Exact Calculation Using a Calculator** **Given:** - **Annual Income:** \$69,800 - **Weeks per Year:** 50 - **Hours per Week:** 40 **Steps:** 1. **Calculate Total Annual Hours:** \[ 50 \text{ weeks/year} \times 40 \text{ hours/week} = 2,000 \text{ hours/year} \] 2. **Calculate Exact Hourly Wage:** \[ \frac{\$69,800}{2,000 \text{ hours}} = \$34.90 \text{ per hour} \] 3. **Round to the Nearest Dollar:** \[ \$34.90 \approx \$35 \] **Exact Hourly Wage:** **\$35** --- ### **3. Comparison of Estimate and Exact Answer** - **Estimated Hourly Wage:** \$35 - **Exact Hourly Wage:** \$35 **Conclusion:** The estimate of \$35 per hour is **exactly** the same as the calculated hourly wage. Therefore, the estimation method used is highly **reasonable and accurate**.