average questions

Nazish · #1 $Old$ 11-06-2008, 03:55 AM

the average of 13 results is 68.the average of first 7 is 63 and that of the last seven is 70,the seventh result is...?

CaptainBlack · #2 $Old$ 11-06-2008, 05:22 AM

Quote:

Originally Posted by Nazish $View Post$

the average of 13 results is 68.the average of first 7 is 63 and that of the last seven is 70,the seventh result is...?

Let the results be $x_1, .. x_{13}$

So

$S_1=\sum_{i=1}^{13} x_i=13 \times 68$

$S_2=\sum_{i=1}^{7} x_i=7 \times 63$

$S_3=\sum_{i=7}^{13} x_i=7 \times 70$

and:

$S_2+S_3=S_1+x_7$

CB

HallsofIvy · #3 $Old$ 11-06-2008, 05:23 AM

Quote:

Originally Posted by Nazish $View Post$

the average of 13 results is 68.the average of first 7 is 63 and that of the last seven is 70,the seventh result is...?

Call the numbers a1, a2, ..., a13.

(a1+ a2+ ...+ a13)/13= 68 so a1+ a2+ ...+ a13= 68(13)= 884

(a1+ a2+ ...+ a7)/7= 63 so a1+ a2+ ....+ a7= 63(7)= 441

(a7+ a8+ ...+ a13)/7= 70 so a7+ a8+ ...+ a13= 70(7)= 490.

Adding those last two results,
a1+ a2+ ...+ 2a7+ a8+ ...+ a13= 441+ 490= 931

But a1+ a2+ ...+ 2a7+ a8+ ...+ a13= (a1+ a2+.a7..+ a13)+ a7= 884+ a7 so
884+ a7= 931. a7= 931- 884= 47.