Question

The average temperature for Wednesday, Thursday and Friday was 42 Deg c. The average for Thursday, Friday and Saturday was 43 Deg c. If the temperature on Saturday was 44 Deg c, what was the temperature on Wednesday?

Answer 1

Hint: This is an arithmetic problem. This problem is based on a simple arithmetic algebraic problem, to find the unknown value, which is done by assigned particular variables to the value which has to be found out yet and then try to get an expression where some simple substitutions and further simplifications can be made to get the result.

Complete step-by-step solution:
Average is the ratio of sum of the values to the total number of values.
Let the value of temperature on Wednesday be : ${T_{Wed}}$
The value of temperature on Thursday be : ${T_{Thu}}$
The value of temperature on Friday be : ${T_{Fri}}$
The value of temperature on Saturday be : ${T_{Sat}}$
First given that the average of the temperature for Wednesday, Thursday and Friday was 42 Deg c, expressing it mathematically :
$ \Rightarrow \dfrac{{{T_{Wed}} + {T_{Thu}} + {T_{Fri}}}}{3} = {42^ \circ }C$
Let ${T_{Thu}} + {T_{Fri}} = x$;
$ \Rightarrow \dfrac{{{T_{Wed}} + x}}{3} = {42^ \circ }C$
Now given that the average for Thursday, Friday and Saturday was 43 Deg c, expressing them mathematically :
$ \Rightarrow \dfrac{{{T_{Thu}} + {T_{Fri}} + {T_{Sat}}}}{3} = {43^ \circ }C$
$ \Rightarrow \dfrac{{x + {T_{Sat}}}}{3} = {43^ \circ }C$
Given that the temperature on Saturday was 44 Deg c :
$ \Rightarrow {T_{Sat}} = {44^ \circ }C$
Substituting ${T_{Sat}}$ in the expression $\dfrac{{x + {T_{Sat}}}}{3} = {43^ \circ }C$, to find out the value of $x$:
$ \Rightarrow \dfrac{{x + {{44}^ \circ }C}}{3} = {43^ \circ }C$
$ \Rightarrow x + {44^ \circ }C = 3({43^ \circ }C)$
$ \Rightarrow x = {129^ \circ }C - {44^ \circ }C$
$ \Rightarrow x = {85^ \circ }C$
Now substituting the value $x = {85^ \circ }C$ in the expression $\dfrac{{{T_{Wed}} + x}}{3} = {42^ \circ }C$, to find out ${T_{Wed}}$:
$ \Rightarrow \dfrac{{{T_{Wed}} + {{85}^ \circ }C}}{3} = {42^ \circ }C$
$ \Rightarrow {T_{Wed}} + {85^ \circ }C = 3({42^ \circ }C)$
$ \Rightarrow {T_{Wed}} = {126^ \circ }C - {85^ \circ }C$
$ \Rightarrow {T_{Wed}} = {41^ \circ }C$
$\therefore {T_{Wed}} = {41^ \circ }C$, the temperature on Wednesday is ${41^ \circ }C.$

The temperature on Wednesday is ${41^ \circ }C.$

Note: Here in this problem, a single variable is assigned to both the temperatures or the sum of the temperature of ${T_{Thu}}$ and ${T_{Fri}}$, so as to make the process easy.