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 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 .
(Round to the nearest dollar as needed.)

Question

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

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

.
(Round to the nearest dollar as needed.)

UpStudy AI · Accepted Answer

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**.
The estimated hourly wage is \$35, which matches the exact calculation of \$35.

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