To determine Mike's total earnings for the week, we need to calculate the regular and shift premium hours for each day, and then use the given rates to find the total earnings.
1. Monday: 12 PM - 7 PM
- There are no hours after 8 PM.
- Regular hours: [tex]\( 7 - 12 = 7 \)[/tex] hours.
- Shift premium hours: [tex]\( 0 \)[/tex] hours.
- Earnings: [tex]\( 7 \times 12.50 = \$87.50 \)[/tex].
2. Tuesday: 9 AM - 5 PM
- There are no hours after 8 PM.
- Regular hours: [tex]\( 17 - 9 = 8 \)[/tex] hours (as 5 PM is 17 in 24-hour format).
- Shift premium hours: [tex]\( 0 \)[/tex] hours.
- Earnings: [tex]\( 8 \times 12.50 = \$100.00 \)[/tex].
3. Wednesday: 6 PM - 11 PM
- Hours worked from 8 PM to 11 PM: [tex]\( 11 - 20 = 3 \)[/tex] hours.
- Regular hours: [tex]\( 20 - 18 = 2 \)[/tex] hours.
- Total worked hours: [tex]\( 5 = 2 + 3 \)[/tex] hours.
- Earnings: [tex]\( (2 \times 12.50) + (3 \times (12.50 + 7)) = 25 + (3 \times 19.50) = 25 + 58.50 = \$83.50 \)[/tex].
4. Thursday: 12 PM - 8 PM
- There are no hours after 8 PM.
- Regular hours: [tex]\( 20 - 12 = 8 \)[/tex] hours.
- Shift premium hours: [tex]\( 0 \)[/tex] hours.
- Earnings: [tex]\( 8 \times 12.50 = \$100.00 \)[/tex].
5. Friday: 3 PM - 9 PM
- Hours worked from 8 PM to 9 PM: [tex]\( 1 \)[/tex] hour.
- Regular hours: [tex]\( 20 - 15 = 5 \)[/tex] hours.
- Total worked hours: [tex]\( 6 = 5 + 1 \)[/tex] hours.
- Earnings: [tex]\( (5 \times 12.50) + (1 \times (12.50 + 7)) = 62.50 + 19.50 = \$82.00 \)[/tex].
Total Earnings Calculation:
- Monday: \[tex]$87.50
- Tuesday: \$[/tex]100.00
- Wednesday: \[tex]$83.50
- Thursday: \$[/tex]100.00
- Friday: \[tex]$82.00
Sum Total Earnings:
\[
87.50 + 100.00 + 83.50 + 100.00 + 82.00 = \$[/tex]453.00
\]
So, Mike's total earnings for the week amount to [tex]\(\$303.00\)[/tex].
