SOLUTION: P=The average of a and b Q=The average of b and c R=The average of c and a The various averages(arithmetic mean) of two of the three numbers a,b,and c are calculated and arra

Algebra ->  Expressions -> SOLUTION: P=The average of a and b Q=The average of b and c R=The average of c and a The various averages(arithmetic mean) of two of the three numbers a,b,and c are calculated and arra      Log On


   

Question 1043301: P=The average of a and b
Q=The average of b and c
R=The average of c and a
The various averages(arithmetic mean) of two of the three numbers a,b,and c are calculated and arranged as shown above. If P>Q>R which of the following is true?
A) a=b=c
B) a>b>c
C) c>b>a
D) b>a>c
Found 2 solutions by Edwin McCravy, robertb:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Just take an example and see:

Take some easy numbers 2,4,6

The average of 2&4 is 3
The average of 4&6 is 5
The average of 2&6 is 4

5 > 4 > 3

So we let P=5, Q=4, R=3, so that P > Q > R

That means:

average of 4&6 > average of 2&6 > average of 2&4

So we have to let a=4, b=6, c=2

And since 6 > 4 > 2, that means b > a > c, choice D

Edwin

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
P > Q > R
<===> %28a%2Bb%29%2F2+%3E+%28b%2Bc%29%2F2+%3E+%28a%2Bc%29%2F2
===> a+b > b+c > a+c
<===> a+b > b+c & b+c > a+c
<===> a > c & b > a
<===> b > a > c.