Final answer:
Gary worked 54 hours this week. Arithmetically, this was calculated by subtracting his weekly salary from his total earnings and then dividing by his hourly wage. Algebraically, this was shown by setting up an equation to solve for the number of hours he worked using the same operations.
Step-by-step explanation:
Calculating Hours Worked Based on Total Earnings
To determine the number of hours Gary worked, we first consider his weekly salary and hourly wage. He earns $17.25 per hour on top of a weekly salary of $45. We can represent Gary's total earnings (T) for the week with the formula T = ($17.25 × hours) + $45.
If Gary earned $976.50 this week, we can set up the following equation to find the number of hours he worked:
$976.50 = ($17.25 × hours) + $45
First, we subtract the fixed weekly salary from the total earnings:
$976.50 - $45 = $931.50
Next, we divide the remaining amount by the hourly rate to find the number of hours:
$931.50 / $17.25 = 54 hours worked
Arithmetically, we have now found that Gary worked for 54 hours during this week.
To solve algebraically, we represent the number of hours as h and set up an equation:
$976.50 = ($17.25 × h) + $45
Solving for h, we subtract $45 from both sides:
$976.50 - $45 = $17.25 × h
Then divide both sides by $17.25:
$931.50 / $17.25 = h
Thus, we find h to be 54 hours.
Both the arithmetic and algebraic methods confirmed that Gary worked 54 hours.