1. **Problem statement:** Calculate the wage for a mechanic who works a 12-hour day with a normal pay rate of 42.50 per hour. 2. **Rules:** - Normal pay rate applies for the first 7 hours. - Overtime pay at time-and-a-half (1.5 times normal rate) applies for the next 2 hours. - Double time (2 times normal rate) applies for any hours beyond 9 hours. 3. **Step 1: Calculate normal pay for 7 hours:** $$7 \times 42.50 = 297.50$$ 4. **Step 2: Calculate overtime pay for next 2 hours at time-and-a-half:** $$2 \times (1.5 \times 42.50) = 2 \times 63.75 = 127.50$$ 5. **Step 3: Calculate double time pay for remaining hours:** Total hours = 12 Hours beyond 9 = 12 - 9 = 3 Double time pay: $$3 \times (2 \times 42.50) = 3 \times 85 = 255$$ 6. **Step 4: Add all pay amounts:** $$297.50 + 127.50 + 255 = 680$$ 7. **Answer:** The mechanic's wage for the 12-hour day is **680**.