Q23. - Algebra 2

Question

Compare the quantity in Column A and the quantity in Column B. Then determine whether:

 

A. the quantity in Column A is greater;

 

B. the quantity in Column B is greater;

 

C. the two quantities are equal;

 

D. the relationship cannot be determined from the information given.

 

23. 

 

The average (arithmetic mean) of $\text{s}$ and $\text{t}$ is greater than the average of $\text{s}$ and $\text{w}$  

 

Column A     Column B

 

     $\text{w}$                   $\text{t}$

Step-by-Step Solution

Answer

The quantity in Colum B is greater than the quantity in Column A. So, the correct option is B.

Step 1 - Consider the two quantities.

The average (arithmetic mean) of s and t is greater than the average of s and w.

 

The quantity in column A is:

 

$w$

 

The quantity in column B is:

 

$t$

Step 2 - Evaluate the two quantities.

Average is defined as sum of the observations divide by the number of observation.

 

The average of $s$ and $t$ is $\frac{s+t}{2}$.

 

And the average of s and w is $\frac{s+w}{2}$.

 

Now, since $\frac{s+t}{2}>\frac{s+w}{2}$, then,

 

$\begin{array}{c}\frac{s+t}{2}>\frac{s+w}{2}\\ \frac{s+t}{2}\times 2>\frac{s+w}{2}\times 2\\ s+t>s+w\\ s+t-s>s+w-s\\ t>w\end{array}$

 

Thus, $t>w$ that is quantity in column B is greater than quantity in column A.

Step 3 - State the conclusion.

The quantity in column B is greater than quantity in column A. Therefore, option B is correct.