Answer:
Cerian is 28 years old
Step-by-step explanation:
The given parameters are;
The average age of the staffs in the mathematics department = 40
The number of staffs in the department = 7
The average age of Jill, Nicky and Wendy = 41
The average age of Andy, Alan and Cathy = 43
From the given parameters, we have;
The average age of the staffs in the mathematics department = (The sum total of the ages of the members of the math department)/(The number of staffs in the department)
Therefore;
40 = (The sum total of the ages of the members of the math department)/ (7)
From which we have;
The sum total of the ages of the members of the math department = 40 × 7 = 280
Which gives;
Jill's age + Nicky's age + Wendy's age + Cathy's age + Cerian's age + Alan's age + Andy's age = 280 years
The average age of Jill, Nicky and Wendy = 41
Given that Jill, Nicky, and Wendy make up 3 of the 7 members of staffs, we have;
The average age of Jill, Nicky and Wendy = (The sum total of the ages of Jill, Nicky, and Wendy)/(The number of staff Jill, Nicky, and Wendt make)
Therefore;
The sum total of the ages of Jill, Nicky, and Wendy = 41 × 3 = 123
Which gives;
Jill's age + Nicky's age + Wendy's age = 123 years
Similarly, the sum total of the ages of Andy, Alan, and Cathy = 43 × 3 = 129
Which gives;
Andy's age + Alan's age + Cathy's age = 129 years
Therefore;
Cerian's age = (Jill's age + Nicky's age + Wendy's age + Cathy's age + Cerian's age + Alan's age + Andy's age) - (Jill's age + Nicky's age + Wendy's age) + (Andy's age + Alan's age + Cathy's age)
∴ Cerian's age = 280 years - 123 years - 129 years = 28 years
</span>