Question

The average of five numbers is $51$. If average of first three number is $42$ and average of last three numbers is $59$. Find the third number.

Answer 1

Given that average of five numbers is $51$

Let $x_1,x_2,x_3,x_4,x_5$ be five numbers

we know average $=\frac{sumofnumbers}{No"ofnumbers}$

$51=\frac{sumof5numbers}{5}$

Sum of $5$ numbers $=51\times 5=255$

$(x_1+x_2+x_3+x_4+x_5)$ __(1)

and the average of first three numbers is $42$

i.e $\frac{x_1+x_2+x_3}{3}=42$

$x_1+x_2+x_3=126$

(sum of first 3 numbers) $=126$ __(2)

and average of last three numbers is $59$

i.e $\frac{x_3+x_4+x_5}{3}=59$

$x_3+x_4+x_5=177$

Sum of last 3 numbers $=177$ __(3)

adding (2) and (3)

$x_1+x_2+x_3+x_3+x_4+x_5=126+177$

$x_1+x_2+x_3+x_4+x_5+x_3=303$ from (1)

$x_1+x_2+x_3+x_4+x_5+x_3=303$

$255+x_3=303$

$x_3=303-255$

$x_3=48$

Third number $=48$