Question 1068851
For any set of numbers, average = (sum of the values)/(number of values), so for the ages of 5 teachers, {{{average = sum/5}}} <--> {{{5*average=sum}}} .
The sum of the 5 teachers ages was
{{{5*48=240}}} .
 
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 {{{46}}} ,
soI know that the sum of those 5 teachers' ages is
{{{sum=5*46=230}}} .
That is {{{240-230=10}}} less than the sum was before,
so the new teacher must be {{{10}}} years younger than the one who retired.
The age of the new teacher is {{{56-10=highlight(46)}}} .
 
THE ALGEBRA STUDENT'S THINKING:
After a teacher of age 56 retired,
the sum of the ages of the remaining 4 teachers was
{{{240-56=184}}} .
After new teacher of age {{{x}}} 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 {{{sum=184+x}}} ,
and the average is now {{{(184+x)/5=46}}} .
That is the equation we need to solve.
{{{(184+x)/5=46}}}
{{{184+x=46*5}}}
{{{184+x=230}}}
{{{x=230-184}}}
{{{highlight(x=46)}}}
Now that I know algebra,
I am really going to be able to answer
all those tricky SAT questions quickly.