The 5 employees at Jewelry Hut are scheduled to work an average of 31 hours each next week, as shown below.
Alan
Susan
Employee Hours Scheduled
24
39
Craig
24
Mary
Scott
40
28
The store manager is hiring two new employees. What number of hours could the manager schedule the new employees to work next week without changing the average number of hours worked by Jewelry Hut employees?
O A. Nate (31 hours) and Lisa (35 hours)
B. Nate (20 hours) and Lisa (24 hours)
O c. Nate (26 hours) and Lisa (30 hours)
O D. Nate (30 hours) and Lisa (32 hours)
To find the number of hours the manager could schedule the new employees to work without changing the average number of hours, we need to calculate the current total number of hours worked by the employees and the average.
The hours scheduled for the current employees are:
Alan: 24 hours
Susan: 39 hours
Craig: 24 hours
Mary: 40 hours
Scott: 28 hours
The total number of hours scheduled for the current employees is:
24 + 39 + 24 + 40 + 28 = 155 hours
The number of current employees is 5.
Therefore, the average number of hours worked by the current employees is:
155 hours / 5 = 31 hours
To maintain the average number of hours at 31, the new employees' hours must also contribute to a total of 31 hours.
Let's assume the hours for the new employees are Nate and Lisa:
Nate: X hours
Lisa: Y hours
The total number of hours after adding the new employees must be equal to:
155 hours + X hours + Y hours = 31 hours * 7 (for 7 employees)
155 + X + Y = 217
Now we need to find two numbers, X and Y, that satisfy this equation and do not change the average.
From the given options, the only combination that satisfies the equation and does not change the average is option C:
Nate (26 hours) and Lisa (30 hours)
So the correct answer is option C.
To find the number of hours the manager can schedule the new employees without changing the average number of hours worked, we need to calculate the current total number of hours worked and the current number of employees.
We have the following information:
Alan: 24 hours
Susan: 39 hours
Craig: 24 hours
Mary: 40 hours
Scott: 28 hours
To calculate the current total number of hours worked, we sum up the hours of each employee:
Total hours = 24 + 39 + 24 + 40 + 28 = 155
To calculate the current number of employees, we count the number of employees:
Number of employees = 5
The average number of hours worked by Jewelry Hut employees is:
Average hours = Total hours / Number of employees = 155 / 5 = 31 hours
Now, we can calculate the maximum total hours the manager can schedule for the new employees without changing the average.
The total number of hours worked by the new employees must be:
Total hours of new employees = Total hours + Total hours of new employees
The total number of employees after hiring the new employees will be:
Total number of employees = Number of employees + Number of new employees
To keep the average number of hours worked the same, the average hours should be:
Average hours = (Total hours + Total hours of new employees) / (Number of employees + Number of new employees) = Average hours
Let's go through the options and see which one meets the criteria:
Option A: Nate (31 hours) and Lisa (35 hours)
Total hours of new employees = 31 + 35 = 66
Total number of employees = 5 + 2 = 7
Average hours = 221 / 7 = 31.57 (not the same as the current average)
Option B: Nate (20 hours) and Lisa (24 hours)
Total hours of new employees = 20 + 24 = 44
Total number of employees = 5 + 2 = 7
Average hours = 199 / 7 = 28.43 (not the same as the current average)
Option C: Nate (26 hours) and Lisa (30 hours)
Total hours of new employees = 26 + 30 = 56
Total number of employees = 5 + 2 = 7
Average hours = 211 / 7 = 30 (the same as the current average)
Option D: Nate (30 hours) and Lisa (32 hours)
Total hours of new employees = 30 + 32 = 62
Total number of employees = 5 + 2 = 7
Average hours = 217 / 7 = 31 (the same as the current average)
Therefore, the correct answer is option D: Nate (30 hours) and Lisa (32 hours).