To determine the amount of the hourly raise, follow these steps:
1. Identify the current hourly wage: The worker currently earns [tex]\(\$27.50\)[/tex] per hour.
2. Convert the percentage to a decimal: The pay raise is given as [tex]\(7 \frac{1}{2} \%\)[/tex]. To convert this percentage into a decimal:
[tex]\[
7 \frac{1}{2} \% = 7.5\% = \frac{7.5}{100} = 0.075
\][/tex]
3. Calculate the hourly raise: Multiply the current hourly wage by the decimal form of the percentage raise to find the increase in the hourly wage.
[tex]\[
\text{Hourly Raise} = 27.50 \times 0.075
\][/tex]
4. Perform the multiplication:
[tex]\[
27.50 \times 0.075 = 2.0625
\][/tex]
5. Round to the nearest cent: Since financial calculations are generally rounded to the nearest cent, round [tex]\(2.0625\)[/tex] to the nearest hundredth.
[tex]\[
2.0625 \approx 2.06
\][/tex]
Thus, the amount of her hourly raise is [tex]\(\$2.06\)[/tex].
