Difference between revisions of "2001 AIME I Problems/Problem 2"

m
(Solution)
Line 3: Line 3:
  
 
== Solution ==
 
== Solution ==
{{solution}}
+
Let x be the mean of S. Let a be the number of elements in S.
 +
Then,
 +
<cmath>\FRAC{ax+1}{a+1}=x-13</cmath>
 +
<cmath>\FRAC{ax+2001}{a+1}=x+27</cmath>
  
 
== See Also ==
 
== See Also ==
 
{{AIME box|year=2001|n=I|num-b=1|num-a=3}}
 
{{AIME box|year=2001|n=I|num-b=1|num-a=3}}

Revision as of 21:54, 21 December 2007

Problem

A finite set $\mathcal{S}$ of distinct real numbers has the following properties: the mean of $\mathcal{S}\cup\{1\}$ is $13$ less than the mean of $\mathcal{S}$, and the mean of $\mathcal{S}\cup\{2001\}$ is $27$ more than the mean of $\mathcal{S}$. Find the mean of $\mathcal{S}$.

Solution

Let x be the mean of S. Let a be the number of elements in S. Then,

\[\FRAC{ax+1}{a+1}=x-13\] (Error compiling LaTeX. ! Undefined control sequence.)
\[\FRAC{ax+2001}{a+1}=x+27\] (Error compiling LaTeX. ! Undefined control sequence.)

See Also

2001 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions
Invalid username
Login to AoPS