Question

The average temperature of the first three days of a week is ${27^ \circ }C$ and the next three days is ${29^ \circ }C$ . If the weekly average is ${28.5^ \circ }C$. What is the temperature on the last day?

Answer 1

Hint: Let the temperature of last day be $x$. Given ${27^ \circ }C$ is the average of first 3 days so from this we can calculate the sum of 3 days temperatures as ${27^ \circ }C \times 3$ same for the next 3 days ${29^ \circ }C \times 3$ after this we know the average of 7 day substitute the sum of 6 days and get the value of last day temperature.

Complete step-by-step answer:
Let the temperature of last day be $x$
Given average temp of 7 days is ${28.5^ \circ }C$=sum temperatures of 7 days divided by 7
Now, it is given that average temperature of the first three days of a week is ${27^ \circ }C$
$ \Rightarrow \dfrac{{{\text{sum of temperature of 3 days}}}}{3} = {27^ \circ }$
Therefore, sum of temperature of 3 days=${27^ \circ }C \times 3 = {81^ \circ }C$
And the next three days is ${29^ \circ }C$
$ \Rightarrow \dfrac{{{\text{sum of temperature of 3 days}}}}{3} = {29^ \circ }$
Therefore, sum of temperature of next 3 days =${29^ \circ }C \times 3 = {87^ \circ }C$
Now, average of I week=${28.5^ \circ }C$
$ \Rightarrow \dfrac{{{{81}^ \circ }C + {{87}^ \circ }C + x}}{7} = {28.5^ \circ }C$
On solving we will get the value of $x$
So, last day temperature will we equal to ${31.5^ \circ }C$

Note: Average is defined as the sum of numbers event divided by the total no. of event. $Average = \dfrac{{{\text{sum of the event}}}}{{{\text{total no}}{\text{. of event}}}}$
Units must be taken care.