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 \( \$ 35 \). (Round to the nearest dollar as needed.) Use 52 weeks a year to find the actual hourly wage. The actual hourly wage is \( \$ 33.56 \). (Round to the nearest cent as needed.) How reasonable is your estimate when compared to the actual answer? Select the correct answer below and fill in the answer box to complete your choice. (Round to the nearest cent as needed.) A. The estimate is a little lower than the actual result. The difference is \( \$ \square \) per hour. B. The estimate is a little higher than the actual result. The difference is \( \$ \square \) per hour. B. . .
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Let's break it down in a fun way! First, rounding the annual income of \( \$ 69,800 \) to the nearest ten thousand gives us \( \$ 70,000 \). Dividing that by the estimated 50 weeks, we find the weekly income is \( \$ 1,400 \), which leads to an estimated hourly wage of about \( \$ 35 \) (since \( 1,400 / 40 = 35 \)). Now, for the actual calculation using 52 weeks: \( 69,800 / (40 \times 52) = 33.56 \) per hour. Comparing the two, your estimate of \( \$ 35 \) is a bit higher than the actual \( \$ 33.56 \). So, the answer is: B. The estimate is a little higher than the actual result. The difference is \( \$ 1.44 \) per hour. You nailed the estimate though—close enough!
