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 $49,600 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 $ 25
(round to the nearest dollar as needed.)
use 52 weeks a year to find the actual hourly wage. the actual hourly wage is $
(round to the nearest cent as needed.)

Explanation:

Step1: Identify the formula for hourly wage

To find the actual hourly wage, we use the formula: Hourly Wage = Annual Income / (Number of Weeks per Year × Hours per Week). Here, Annual Income = $49,600, Number of Weeks per Year = 52, Hours per Week = 40.

Step2: Calculate the denominator

First, calculate the total number of hours worked in a year: \( 52 \times 40 = 2080 \) hours.

Step3: Divide annual income by total hours

Now, divide the annual income by the total number of hours: \( \frac{49600}{2080} \). Let's simplify this division. We can divide numerator and denominator by 10: \( \frac{4960}{208} \). Then divide numerator and denominator by 8: \( \frac{620}{26} \). Divide numerator and denominator by 2: \( \frac{310}{13} \approx 23.846 \). Rounding to the nearest cent, we get approximately $23.85. Wait, but let's check the calculation again. Wait, 49600 divided by 2080: 2080 × 23 = 47840, 49600 - 47840 = 1760. 1760 / 2080 = 0.846. So total is 23.846, which rounds to $23.85? Wait, but maybe I made a mistake. Wait, 52 weeks × 40 hours = 2080 hours. 49600 ÷ 2080: let's do 49600 ÷ 2080. Divide numerator and denominator by 10: 4960 ÷ 208. 208 × 23 = 4784, 4960 - 4784 = 176. 176 ÷ 208 = 11/13 ≈ 0.846. So 23.846, which is $23.85 when rounded to the nearest cent. Wait, but the estimate was $25. Let's see the estimate: round annual income to nearest ten thousand: 49600 rounds to 50000. Number of weeks estimated as 50. So estimate: 50000 / (50 × 40) = 50000 / 2000 = 25. Which matches the given estimate. Now the actual calculation: 49600 / (52×40) = 49600 / 2080 = 23.84615... So approximately $23.85. Wait, but maybe I miscalculated. Wait, 52×40 is 2080. 49600 ÷ 2080: 2080 × 24 = 49920, which is more than 49600. So 23.846, so $23.85. But let's check with a calculator: 49600 ÷ 2080 = 23.8461538... So rounding to the nearest cent is $23.85. Wait, but the problem says "the actual hourly wage is $□". Wait, maybe I made a mistake in the steps. Wait, let's recalculate: 52 weeks × 40 hours = 2080 hours. 49600 divided by 2080: 2080 × 23 = 47840, 49600 - 47840 = 1760. 1760 / 2080 = 0.846. So 23.846, which is $23.85. But maybe the problem expects a different approach? Wait, no, the formula is correct: hourly wage = annual income / (weeks × hours per week). So the actual hourly wage is approximately $23.85. Wait, but let's check again. 49600 ÷ 52 = 953.84615... (weekly wage), then divide by 40: 953.84615 ÷ 40 = 23.84615... So yes, $23.85.

Answer:

\( \$23.85 \)