Brianna works as an interpreter for her city government. She bills $11.25 per quarter-hour or any part of a quarter-hour. Last month, she provided services four times, for 5 hours and 23 minutes, 4 hours and 12 minutes, 5 hours and 38 minutes, and 1 hour and 49 minutes, respectively.

Question

How much did Brianna bill for all four sessions last month?
$

Answer 1

To calculate Brianna's total bill for her interpreting services last month, we first need to convert the total time worked into quarter-hours and then multiply it by her rate of $11.25.

1. Convert each session's time into total minutes:

   • 5 hours and 23 minutes = \(5 \times 60 + 23 = 300 + 23 = 323\) minutes
   • 4 hours and 12 minutes = \(4 \times 60 + 12 = 240 + 12 = 252\) minutes
   • 5 hours and 38 minutes = \(5 \times 60 + 38 = 300 + 38 = 338\) minutes
   • 1 hour and 49 minutes = \(1 \times 60 + 49 = 60 + 49 = 109\) minutes

2. Calculate the total minutes for all sessions: \[ 323 + 252 + 338 + 109 = 1022 \text{ minutes} \]

3. Convert total minutes into quarter-hours:

   • There are 15 minutes in a quarter-hour. To find the total number of quarter-hours, we divide the total minutes by 15: \[ \frac{1022}{15} = 68.1333 \] Since she bills for any part of a quarter-hour, we round this up to the next whole number, which is 69 quarter-hours.

4. Calculate the total bill: \[ 69 \times 11.25 = 776.25 \]

Thus, Brianna billed a total of $776.25 for all four sessions last month.