Question

One week Sam worked 32.75 hours at his job, which pays \(\$ 17.50\) per hour. How much did he earn that week before taxes and other deductions? Round to the nearest cent. A. \(\$ 50.25\) B. \(\$ 560.00\) C. \(\$ 573.13\) D. \(\$ 5,731.25\)

Short answer

573.13

Step-by-step solution

Identify Given Values

Sam worked 32.75 hours in one week, and his pay rate is \(\text{\textdollar} 17.50\) per hour.

Write the Formula

The formula to calculate earnings is: \( \text{Earnings} = \text{Hours Worked} \times \text{Hourly Rate} \).

Substitute the Values

Substitute the given values into the formula: \( \text{Earnings} = 32.75 \times 17.50 \).

Perform the Multiplication

Multiply the values: \( 32.75 \times 17.50 = 573.125 \).

Round to the Nearest Cent

Round the result to the nearest cent: \( 573.125 \) rounds to \( 573.13 \).

Verify the Answer

Out of the given options, the earnings match option C: \( \text{\textdollar} 573.13 \).

Key concepts

hourly wage calculation

To start understanding how to calculate hourly wages, you first need to know two key pieces of information: the number of hours worked and the hourly rate of pay. In Sam's case, he worked for 32.75 hours, and his hourly wage is \( \$17.50 \). The formula to find the earnings is quite straightforward: \[ \text{Earnings} = \text{Hours Worked} \times \text{Hourly Rate} \].

Think of this as multiplying the number of hours you have worked by how much you get paid for one hour. This simple multiplication will give you the total amount earned over that period. For instance, if someone worked 10 hours at \(\$20\) per hour, they would earn \(10 \times 20 = \$200\).
Sam's weekly earnings can be calculated using the exact same formula. Just plug in the values he has: \( 32.75 \text{ hours} \times \$17.50 \text{ per hour} \). The result you get here is the total payment before taxes and deductions.

rounding to nearest cent

Rounding to the nearest cent is an essential skill because it ensures that your calculations, especially in financial contexts, are precise and user-friendly. When you calculate Sam's earnings, you get a number like 573.125. This number needs rounding because dealing with more than two decimal places isn’t practical, especially in currency.

To round to the nearest cent (which is two decimal places), you look at the third decimal place to decide if you should round up or down. If the third decimal is 5 or above, you round up. If it is less than 5, you round down.
For example:

• If the number is 57.435, it rounds to 57.44 (because 5 is above 4).
• If the number is 57.432, it rounds to 57.43 (because 2 is less than 5).

In Sam's case: \(573.125\) becomes \(573.13\) since the third decimal place (5) implies rounding up the second decimal place to 3.

multiplication in decimal numbers

Multiplication involving decimal numbers can be challenging, but with practice, it becomes straightforward. When multiplying decimals, you essentially perform the multiplication as if both numbers were whole numbers and then place the decimal point in the result.

Here's a step-by-step approach:

• Multiply the numbers as if they were whole numbers. For instance, multiply 3275 (32.75 without the decimal) by 1750 (17.50 without the decimal).
• Count the total number of decimal places in both original numbers. In this case, 32.75 has two decimal places, and 17.50 has two, so combined they total four decimal places.
• Place the decimal in your result such that there are four decimal places. For example, if the raw multiplication gives you 5731250, you place the decimal to get 573.1250 (line up with four places).

After you get the product, you follow the rounding rules to round it to the nearest cent, which we’ve already discussed.
In Sam's case: \(32.75 \times 17.50 = 573.125\). Then, rounding it up, you get \(\$573.13\), confirming the right answer.