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A certain corporation has software that calculates the cost of a meeting. The software multiplies the hourly salary for each employee attending the meeting by the number of hours that the employee spends at the meeting. The cost of the meeting is the sum of those results. One manager has used another method to calculate the cost of a meeting. The manager takes the average (arithmetic mean) salary of all employees attending the meeting multiplied by the average number of hours that employees spend at the meeting, which is then multiplied by the total number of employees attending the meeting.
Consider the following incomplete statement: The manager's calculation is equal to that of the software when all the employees who attend the meeting 1 at the meeting, or if that is not the case, when all of those employees who attend the meeting 2 Based on the information provided, select for 1 and for 2 the options that create the statement that is most accurate and rhetorically well-constructed. Make only two selections, one in each column.
are managers
are not managers
spend the same amount of time
spend different lengths of time
have the same salary
have different salaries
Let's create a comparison table to understand how each method works:
| Method | Calculation |
| Software | Sum of (Each employee's salary × Their hours) |
| Manager | (Average salary) × (Average hours) × (Number of employees) |
Let's test with 3 employees:
Software calculation:
\(($50 \times 2) + ($100 \times 1) + ($75 \times 3) = $100 + $100 + $225 = $425\)
Manager calculation:
These are different! So when are they equal?
Let's express both methods algebraically:
For these to be equal:
\(\Sigma(\mathrm{salary}_i \times \mathrm{hours}_i) = (\Sigma\mathrm{salary}_i \times \Sigma\mathrm{hours}_i)/n\)
This equality holds in specific cases. Let's test two scenarios:
Scenario 1: All employees spend the same time (t hours)
Scenario 2: All employees have the same salary (s dollars/hour)
We've identified two conditions that make the calculations equal:
Looking at our answer choices:
Statement 1: "spend the same amount of time"
Statement 2: "have the same salary"
These selections create a mathematically accurate statement: The manager's calculation equals the software's when all employees spend the same amount of time at the meeting, or if that's not the case, when all employees have the same salary.