Q9. - Algebra 2

Question

The average (arithmetic mean) of r, s, x and y is 8, and the average of x and y is 4. What is the average of r and s?

$\begin{array}{l}\text{A}.\text{ 4 B. 6}\\ \text{C}.\text{ 8 D. 12}\end{array}$

Step-by-Step Solution

Answer

The average of r and s is 12. Option D is correct.

Step-1 – Apply the concept of arithmetic mean

The arithmetic mean or average of numbers $x_1,x_2,\dots x_n$ is sum of the numbers divided by total count of numbers n. Mathematically, it is expressed below.

$\overline{x}=\frac{x_1+x_2+\dots +x_n}{n}$

Step-2 –Express the data from question

Consider the provided information that average of four numbers r, s, x, and y is 8.

Also, average of x and y is 4.

Express the average of r, s, x, and y as shown below.

$\frac{r+s+x+y}{4}=8$

Multiply both sides by 4.

$r+s+x+y=32$

Express the average x and y as shown below.

$\frac{x+y}{2}=4$

Multiply both sides by 2.

$x+y=8$

Step-3 – Compute average of r and s

The average of r and s is expressed as $\frac{r+s}{2}$.

Substitute $x+y=8$ in the equation $r+s+x+y=32$ and simplify.

$\begin{array}{c}r+s+8=32\\ r+s=32-8\\ r+s=24\end{array}$

Divide both sides by 2.

$\frac{r+s}{2}=12$

Hence, the average of r and s is 12.