A radiologic technologist earns an average salary of \( \$ 21.78 \) per hour for a regular 40 -hour work week. She earns 1.5 times her average rate when she works weekends. Find the total wages earned by the technologist for a week where she works a 40 hour week and 11 hours on the weekend.

**Step 1. Determine the regular hourly wage and weekend hourly wage.** The regular rate is given as \[ \$21.78 \text{ per hour.} \] The weekend rate is 1.5 times the regular rate: \[ 1.5 \times \$21.78 = \$32.67 \text{ per hour.} \] **Step 2. Compute the earnings for the 40-hour regular work week.** Multiply the regular hourly wage by 40 hours: \[ 40 \times \$21.78 = \$871.20. \] **Step 3. Compute the earnings for the 11 weekend hours.** Multiply the weekend hourly wage by 11 hours: \[ 11 \times \$32.67 = \$359.37. \] **Step 4. Compute the total weekly wages.** Add the earnings from the regular hours and the weekend hours: \[ \$871.20 + \$359.37 = \$1230.57. \] Thus, the total wages earned for the week are \[ \$1230.57. \]