The mean age of a class of twenty five students is 23.4 years. How old would a twenty sixth student have to be for the mean age of the class to be 24.0 years?
Well, if the mean age of the current class is 23.4 years and you want it to be 24.0 years, you'll need someone who's age is definitely above average... Personally, I'd suggest finding someone who's been around the block a few more times, like... let's say 50 years old. That would definitely boost the average! But don't forget to make sure they're ready to party with a bunch of rowdy students!
To find out how old the twenty-sixth student would have to be for the mean age of the class to be 24.0 years, we can use the formula for the mean:
Mean = Sum of all ages / Total number of students
Given that the mean age of the class with 25 students is 23.4 years, we can determine the sum of all ages:
Sum of all ages = Mean * Total number of students
= 23.4 * 25
= 585 years
To find the age of the twenty-sixth student, we need to add this student's age to the sum of all ages and then divide by the new total number of students:
(585 + Age of the twenty-sixth student) / (25 + 1) = 24.0
585 + Age of the twenty-sixth student = 24.0 * 26
585 + Age of the twenty-sixth student = 624
Age of the twenty-sixth student = 624 - 585
Age of the twenty-sixth student = 39
Therefore, the twenty-sixth student would have to be 39 years old for the mean age of the class to be 24.0 years.
To find out how old the twenty-sixth student would have to be for the mean age of the class to be 24.0 years, we need to set up an equation.
The mean age of a group of individuals is calculated by dividing the sum of their ages by the number of individuals. In this case, we know that the mean age of the class of twenty-five students is 23.4 years.
So, the total sum of the ages of the twenty-five students can be found by multiplying the mean age (23.4 years) by the number of students (25). This gives us 23.4 * 25 = 585 years.
Now, let's say the age of the twenty-sixth student is x years. To find the new mean age of the class with the twenty-sixth student included, we divide the sum of the ages of all the students by the total number of students, which is 26 now.
So, the equation is:
(585 + x) / 26 = 24.0
To find x, we can solve this equation by multiplying both sides by 26, giving us:
585 + x = 624
Now, subtracting 585 from both sides, we have:
x = 624 - 585
x = 39
Therefore, the twenty-sixth student would have to be 39 years old for the mean age of the class to be 24.0 years.
The sum of ages of the 25 students = 25(23.4) = 585
the sum of ages of 26 students = 26(24) = 624
So the 26th student must be 624-585 or 39 years old