The 5 employees at Jewelry Hut are scheduled to work an average of 31 hours each next week, as shown below.
A table labeled Employee hours scheduled. Alan has 24 hours, Susan has 39 hours, Craig has 24 hours, Mary has 40 hours and Scott has 28 hours.
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?
A.
Nate (31 hours) and Lisa (35 hours)
B.
Nate (20 hours) and Lisa (24 hours)
C.
Nate (26 hours) and Lisa (30 hours)
D.
Nate (30 hours) and Lisa (32 hours)
C. Nate (26 hours) and Lisa (30 hours)
AAAaannndd the bot gets it wrong yet again!
24+39+24+40+28 + x = 7*31
x = 62
so D: 30+32=62
To determine the number of hours the manager can schedule the new employees to work without changing the average number of hours worked, we can solve the following equation:
Total hours scheduled = Average hours per employee * Total number of employees
Let's calculate the total hours scheduled for the current employees:
Total hours scheduled = 24 + 39 + 24 + 40 + 28 = 155 hours
The total number of employees currently is 5.
So, the current average hours per employee are: 155 hours / 5 employees = 31 hours/employee.
To maintain the average of 31 hours, the total hours scheduled for the new employees must be:
Total hours scheduled for new employees = Average hours per employee * Number of new employees
= 31 hours/employee * 2 employees
= 62 hours
Now let's analyze the given options:
A. Nate (31 hours) and Lisa (35 hours) - The total hours scheduled would be 155 + 31 + 35 = 221, which is not equal to the current total hours (155). Incorrect.
B. Nate (20 hours) and Lisa (24 hours) - The total hours scheduled would be 155 + 20 + 24 = 199, which is not equal to the current total hours (155). Incorrect.
C. Nate (26 hours) and Lisa (30 hours) - The total hours scheduled would be 155 + 26 + 30 = 211, which is not equal to the current total hours (155). Incorrect.
D. Nate (30 hours) and Lisa (32 hours) - The total hours scheduled would be 155 + 30 + 32 = 217. This option maintains the current total hours of 155. Correct.
Therefore, the correct option is D. Nate (30 hours) and Lisa (32 hours).
To determine the number of hours the manager could schedule the new employees without changing the average number of hours worked, we need to find the total number of hours worked by the five current employees.
Alan: 24 hours
Susan: 39 hours
Craig: 24 hours
Mary: 40 hours
Scott: 28 hours
To find the total number of hours that the current employees are scheduled to work, we sum up their hours:
24 + 39 + 24 + 40 + 28 = 155 hours
To maintain the average of 31 hours per employee (assuming the two new employees will also work 31 hours each), we need to find the total number of hours for all seven employees:
Average hours per employee * number of employees = total hours
31 hours * 7 employees = 217 hours
Now, we subtract the total hours worked by the current five employees to find the remaining hours available for the new employees:
217 hours - 155 hours = 62 hours
Thus, the manager could schedule the new employees for a total of 62 hours.
Looking at the answer choices:
A. Nate (31 hours) and Lisa (35 hours): The total hours for Nate and Lisa would be 31 + 35 = 66 hours, which exceeds the remaining 62 hours. This option is not valid.
B. Nate (20 hours) and Lisa (24 hours): The total hours for Nate and Lisa would be 20 + 24 = 44 hours, which is less than the remaining 62 hours. This option is valid.
C. Nate (26 hours) and Lisa (30 hours): The total hours for Nate and Lisa would be 26 + 30 = 56 hours, which is less than the remaining 62 hours. This option is valid.
D. Nate (30 hours) and Lisa (32 hours): The total hours for Nate and Lisa would be 30 + 32 = 62 hours, which is equal to the remaining 62 hours. This option is valid.
Therefore, the correct answer is D. Nate (30 hours) and Lisa (32 hours).