Gao earns his regular pay of 12 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Gao is paid 1(1)/(2) times his regular pay. How much does Gao earn in a week in which he works 56 hours?

To find out how much Gao earns in a week in which he works 56 hours, we need to calculate his earnings for the first 40 hours and then calculate his earnings for the additional 16 hours (56 - 40 = 16).<br /><br />First, let's calculate Gao's earnings for the first 40 hours:<br />Earnings for the first 40 hours = Regular pay per hour × Number of hours worked up to 40 hours<br />Earnings for the first 40 hours = $12 × 40<br />Earnings for the first 40 hours = $480<br /><br />Next, let's calculate Gao's earnings for the additional 16 hours:<br />Earnings for the additional 16 hours = Overtime pay per hour × Number of overtime hours<br />Overtime pay per hour = Regular pay per hour × 1\frac{1}{2}<br />Overtime pay per hour = $12 × 1\frac{1}{2}<br />Overtime pay per hour = $18<br />Earnings for the additional 16 hours = $18 × 16<br />Earnings for the additional 16 hours = $288<br /><br />Finally, let's calculate Gao's total earnings for the week:<br />Total earnings = Earnings for the first 40 hours + Earnings for the additional 16 hours<br />Total earnings = $480 + $288<br />Total earnings = $768<br /><br />Therefore, Gao earns $768 in a week in which he works 56 hours.