SOLUTION: S=( 11,12,13,14,15). The median of the set S is equal to the mean of the set T, which consists of 11 consecutive positive integers. What is the largest integer of the set T? A)1

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: S=( 11,12,13,14,15). The median of the set S is equal to the mean of the set T, which consists of 11 consecutive positive integers. What is the largest integer of the set T? A)1      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1143714: S=( 11,12,13,14,15). The median of the set S is equal to the mean of the set T, which consists of 11 consecutive positive integers. What is the largest integer of the set T?
A)19
B)18
C)17
D)16
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

median= the average of the first and the last terms
S=( 11,12,13,14,15).
median=%2811%2B15%29%2F2=13
The median of the set S is equal to the mean of the set T, which consists of 11 consecutive positive integers. What is the largest integer of the set T?
mean of the set T=13
mean= median
the sum of the elements = the mean * # of elements
the sum of the elements = 13+%2A11=143
the sum of the 11+consecutive positive integers:
x%2Bx%2B1%2Bx%2B2%2Bx%2B3%2Bx%2B4%2Bx%2B5%2Bx%2B6%2Bx%2B7%2Bx%2B8%2Bx%2B9%2Bx%2B10=11x%2B55
11x%2B55=143
11x=143-55
11x=88
x=8............smallest integer in the set T,
then the largest integer of the set T is 8%2B10=18
check the median
%288%2B18%29%2F2=36%2F2=13->which is true
so, answer is B) 18

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


In any set of an odd number of consecutive positive integers, the mean and the median are the same.

So we have a set S consisting of 5 consecutive positive integers with a mean of 13; that means a middle number 13 with the 2 integers either side of 13.

We are looking for the largest number in a set T consisting of 11 positive integers with middle number 13. That means middle number 13 with 5 integers either side of 13.

That makes the largest integer in set T 13+5 = 18.