Question

If the average of a, b, c, d, and e is 38, average of a, c, and e is 28, and average of b and d is $n^2+4$, then the value of n is $\pm k$. Find the value of k.

Answer 1

Average of a, b, c, d, and e = 38
i.e., $\frac{a+b+c+d+e}{5}=38$
$\Rightarrow$ a + b + c + d + e = 190 ........ (i)
Average of a, c, and e = 28
i.e., $\frac{a+c+e}{3}=28$
$\Rightarrow$ a + c + e = 84 ........ (ii)
Subtracting (ii) from (i), we get
b + d = 106
Average of b and d $=\frac{b+d}{2}=\frac{106}{2}=53$
$\therefore n^2+4=53\Rightarrow n^2=53-4=49$
$\Rightarrow n=\pm 7$
Since n = $\pm k$, we conclude that k = 7.