Question

The average of 6 numbers is 4. A seventh is added and the new average is 5. Find the seventh number.

Answer 1

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Answer 2

Answer:

The seventh number is 11.

Step-by-step explanation:

given:

The average of 6 numbers is = 4

the average of 7 numbers is = 5

seventh number = ?

let the six numbers be  A,B,C,D,E and F.

and the seventh number be X.

now we have,

   $\frac{A+B+C+D+E+F}{6} = 4$

$A+B+C+D+E+F = 24$   -------------------------------------------( 1 ).

and ,

$\frac{A+B+C+D+E+F+X}{7} = 5$  

$\frac{A+B+C+D+E+F}{7} +\frac{X}{7} = 5$

from equation ( 1 ),

$\frac{24}{7}+ \frac{X}{7} = 5$

$\frac{24 + X}{7} = 5$

24 + X = 35

X = 11.

Thus the seventh number is 11.

Hope it helps !