Final answer:
To find out how many hours were worked, calculate the gross pay by dividing the take-home pay by (1 - tax rate). After determining the gross pay ($660), divide it by the hourly wage ($20) to find the hours worked. The calculation results in 33 hours, which implies Option C: 34 hours could be the correct answer when considering potential rounding.
Step-by-step explanation:
To calculate the number of hours worked, we first need to determine the gross pay before taxes. Since we know the take-home pay and the tax rate, we can find the gross pay by using the formula: take-home pay = gross pay - (gross pay * tax rate). Here, we rearrange the formula to solve for gross pay, which gives us: gross pay = take-home pay / (1 - tax rate).
By inserting the given values, we get: gross pay = $580.80 / (1 - 0.12) which simplifies to gross pay = $580.80 / 0.88, resulting in a gross pay of $660. Now, since the pay rate per hour is $20, we divide the gross pay by the pay rate to find the total hours worked: hours worked = gross pay / pay rate.
Therefore, hours worked = $660 / $20, which equals 33 hours worked. The closest answer to this is option C: 34 hours, which indicates that the student may have worked a fraction of an hour more that is rounded to the nearest whole hour.