SOLUTION: The average age of 5 teachers of a school was 48.From them a teacher of age 56 was retired and a new teacher came.The present average age is 46.What is the age of the new teacher?

Question 1068851: The average age of 5 teachers of a school was 48.From them a teacher of age 56 was retired and a new teacher came.The present average age is 46.What is the age of the new teacher?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
For any set of numbers, average = (sum of the values)/(number of values), so for the ages of 5 teachers, <--> .
The sum of the 5 teachers ages was
.

THE FIFTH GRADER'S SOLUTION:
After new teacher came, there were again 5 teachers,
with 4 teachers that were teachers in the school before,
and the new teacher replacing the one who retired.
The problem tells me that the average for those 5 teachers is now ,
soI know that the sum of those 5 teachers' ages is
.
That is less than the sum was before,
so the new teacher must be years younger than the one who retired.
The age of the new teacher is .

THE ALGEBRA STUDENT'S THINKING:
After a teacher of age 56 retired,
the sum of the ages of the remaining 4 teachers was
.
After new teacher of age came,
there were again 5 teachers,
with 4 teachers that were teachers in the school before,
and the new teacher replacing the one who retired.
The sum of their ages is now ,
and the average is now .
That is the equation we need to solve.

Now that I know algebra,
I am really going to be able to answer
all those tricky SAT questions quickly.
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