Chapter 2: Q9. (page 106)

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

Short Answer

Expert verified

The average of r and s is12. Option D is correct.

Step by step solution

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.

$\bar{x} = \frac{x_{1} + x_{2} + \dots + x_{n}}{n}$

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{matrix} r + s + 8 = 32 \\ r + s = 32 - 8 \\ r + s = 24 \end{matrix}

Divide both sides by 2.

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

Hence, the average of r and s is 12.

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Column A	Column B
The x-coordinate of point Q	The y-coordinate of point P

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

Short Answer

Step by step solution

Step-1 – Apply the concept of arithmetic mean

Step-2 –Express the data from question

Step-3 – Compute average of r and s

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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?A.4B.6C.8D.12

Short Answer

Step by step solution

Step-1 – Apply the concept of arithmetic mean

Step-2 –Express the data from question

Step-3 – Compute average of r and s

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Decision Maths

Calculus

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

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