Chapter 3.6, Problem 38PPS

To determine

To calculate:Have to calculate the total average.

Answer to Problem 38PPS

The total average precipitation that fall in August, September and, October are $\frac{32}{15}$ .

Explanation of Solution

Given:

Month	Amount (in.)
August	$2\frac{47}{50}$
September	$1\frac{22}{25}$
October	$1\frac{1}{2}$

Average: Average is thearithmetic mean, the sum of numbers divided by how many numbers are being average.

Calculation:

  $Average=\frac{August+September+October}{3}\mathrm{...}\left(\text{i}\right)$

Now, $=2\frac{47}{50}+1\frac{22}{25}+1\frac{1}{2}$

  $=\frac{52\times 2+47}{50}+\frac{1\times 25+22}{25}+\frac{1\times 2+1}{2}$

  $=\frac{151}{50}+\frac{47}{25}+\frac{3}{2}\left[\begin{array}{l}\because \begin{array}{cc}5& 50,25,2\\ 5& 10,5,2\\ 2& 2,1,2\\ & 1,1,1\end{array}\\ \text{LCM = 5}\times \text{5}\times \text{2=50}\end{array}\right]$

  $\begin{array}{l}=\frac{151+47\times 2+3\times 25}{50}\\ =\frac{151+94+75}{50}\\ =\frac{320}{50}\\ =\frac{32}{5}\end{array}$

Putting $\frac{32}{5}$ in the equation (i), we get

  $\begin{array}{l}\text{Average}=\frac{\text{August+September+October}}{3}\\ \text{Average}=\frac{\frac{32}{5}}{3}=\frac{\frac{32}{5}}{\frac{3}{1}}\\ \text{Average}=\frac{32}{5}\times \frac{1}{3}=\frac{32\times 1}{5\times 3}\\ \text{Average}=\frac{32}{15}\end{array}$