SOLUTION: The average of 10 numbers is 13. The average of the first 6 numbers is 14 and that of the last 6 numbers is 11. If the sixth number is 1.5 times the fifth number find the avera

Algebra ->  Finance -> SOLUTION: The average of 10 numbers is 13. The average of the first 6 numbers is 14 and that of the last 6 numbers is 11. If the sixth number is 1.5 times the fifth number find the avera      Log On


   



Question 1055431: The average of 10 numbers is 13. The average of the first 6 numbers is 14 and
that of the last 6 numbers is 11. If the sixth number is 1.5 times the fifth number
find the average of those two numbers.
What would be the average of the first four and the last four number.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.%28A%2BB%2BC%2BD%2BE%2BF%2BG%2BH%2BI%2BJ%29%2F10=13
2.%28A%2BB%2BC%2BD%2BE%2BF%29%2F6=14
3.%28E%2BF%2BG%2BH%2BI%2BJ%29%2F6=11
4.F=%283%2F2%29E
From 1,
A%2BB%2BC%2BD%2BE%2BF%2BG%2BH%2BI%2BJ=130
From 2,
A%2BB%2BC%2BD%2BE%2BF=84
Subtracting,
A%2BB%2BC%2BD%2BE%2BF%2BG%2BH%2BI%2BJ-A-B-C-D-E-F=130-84
G%2BH%2BI%2BJ=46
From 3,
E%2BF%2BG%2BH%2BI%2BJ=66
Subtracting again,
E%2BF%2BG%2BH%2BI%2BJ-G-H-I-J=66-46
E%2BF=20
So the average is,
%28E%2BF%29%2F2=10
.
.
.
Going back to this equation,
E%2BF=20
Substitute from 4,
E%2B%283%2F2%29E=20
%285%2F2%29E=20
E=8
So then,
F=%283%2F2%298
F=12
From 2,
A%2BB%2BC%2BD%2BE%2BF=84
Substituting,
A%2BB%2BC%2BD%2B20=84
A%2BB%2BC%2BD=64
So the average of the first four is,
%28A%2BB%2BC%2BD%29%2F4=16
.
.
.
Similarly,
E%2BF%2BG%2BH%2BI%2BJ=66
20%2BG%2BH%2BI%2BJ=66
G%2BH%2BI%2BJ=46
%28G%2BH%2BI%2BJ%29%2F4=46%2F4
%28G%2BH%2BI%2BJ%29%2F4=23%2F2