SOLUTION: The average of four numbers is 24. if the largest number is left out , the average is 20. . if the smallest is left out , the average is 30. what is the average of the middle tw

Algebra ->  Average -> SOLUTION: The average of four numbers is 24. if the largest number is left out , the average is 20. . if the smallest is left out , the average is 30. what is the average of the middle tw      Log On


   

Question 306207: The average of four numbers is 24. if the largest number is left out , the average is 20. . if the smallest is left out , the average is 30. what is the average of the middle two numbers ?
a 25 b 26 c 27 d 28 e none of these

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A,B,C,D be your numbers in increasing value.
%28A%2BB%2BC%2BD%29%2F4=24
%28A%2BB%2BC%29%2F3=20
%28B%2BC%2BD%29%2F3=30
Let's substitute,
Z=B%2BC
.
.
.
1.A%2BZ%2BD=96
2.A%2BZ=60
3.Z%2BD=90
From eq. 2,
A%2BZ=60
A=60-Z
From eq. 3,
Z%2BD=90
D=90-Z
Substitute these into eq. 1,
A%2BZ%2BD=96
%2860-Z%29%2BZ%2B%2890-Z%29=96
150-Z=96
Z=54
So then
B%2BC=54
We're looking for %28B%2BC%29%2F2
%28B%2BC%29%2F2=27
.
.
.
c) is the correct answer.