Chapter 3.6, Problem 51STP

To determine

To find: Average of $r$ and $w$

Answer to Problem 51STP

Average of $r$ and $w$ is $12$ .

Explanation of Solution

Given information:

Average of $r,w,x$ and $y$ is $8$ .

Average of $x$ and $y$ is $4$ .

Calculation:

From given information

Average of $r,w,x$ and $y$ is $8$ .

It means

  $\frac{r+w+x+y}{4}=8$

  $\begin{array}{l}\frac{r+w+x+y}{4}=8\\ \Rightarrow r+w+x+y=8\times 4\\ \Rightarrow r+w+x+y=32\end{array}$

  $r+w+x+y=32$ -------(1)

From given information

Average of $x$ and $y$ is $4$

We get

  $\begin{array}{l}\frac{x+y}{2}=4\\ \Rightarrow x+y=4\times 2\\ \Rightarrow x+y=8\end{array}$

  $x+y=8$ -------(2)

Substituting $x+y=8$ in equation −(1)

We get

  $\begin{array}{l}r+w+x+y=32\\ \Rightarrow r+w+8=32\\ \Rightarrow r+w=32-8\\ \Rightarrow r+w=24\end{array}$

  $r+w=24$ -----(3)

Average of $r$ and $w$ is

Average = $\frac{r+w}{2}$

Substituting $r+w$ value from equation-(3)

We get

  $\Rightarrow$ Average = $\frac{24}{2}$

  $\Rightarrow$ Average = $12$

Therefore,

Average of $r$ and $w$ is $12$