the average age of 30 children in a class is 9 years if the teacher 's age is included, the average age becomes 10 years find the teacher's age
(x + 30(9) )/31 = 10
x + 270 = 310
x = 40
To find the teacher's age, we first need to understand the given information.
We know that the average age of 30 children in the class is 9 years. This means that if we add up the ages of all 30 children and divide the total by 30, we would get an average of 9 years.
Let's denote the sum of the ages of the 30 children as X.
So, the equation would be:
X/30 = 9
Next, we are given that if we include the teacher's age, the average age becomes 10 years. Since now the average is calculated with 31 people (30 children + 1 teacher), we can write:
(X + T)/31 = 10
Where T represents the teacher's age.
Now, we have two equations:
1) X/30 = 9
2) (X + T)/31 = 10
To solve these equations and find the teacher's age, we need to eliminate one of the variables by solving for one of them in terms of the other.
From equation 1), solve for X:
X = 9 * 30
X = 270
Now we can substitute the value of X into equation 2):
(270 + T)/31 = 10
To find the teacher's age, we can multiply both sides of the equation by 31:
270 + T = 10 * 31
270 + T = 310
Now, isolate T by subtracting 270 from both sides:
T = 310 - 270
T = 40
Therefore, the teacher's age is 40 years.