Question

Sneha uses the relationship shown to change between temperature in degrees Fahrenheit \[\left( {^ \circ F} \right)\] and temperature in degrees Celsius \[\left( {^ \circ C} \right)\] . Sasha thinks that \[{30^ \circ }C\] is higher than \[{82^ \circ }F\] . Is she correct? Show how you worked out your answer. Relationship used by Sneha: \[5f = 9C + 160\] where \[f\] is the temperature in degrees Fahrenheit \[\left( {^ \circ F} \right)\] and \[C\] is the temperature in degrees Celsius \[\left( {^ \circ C} \right)\] .

Answer 1

Hint: First, we shall analyze the given information. A relation is given in the question \[5f = 9C + 160\] where \[f\] is the temperature in degrees Fahrenheit \[\left( {^ \circ F} \right)\] and \[C\] is the temperature in degrees Celsius \[\left( {^ \circ C} \right)\] .
   We are asked if the statement \[{30^ \circ }C\] is higher than \[{82^ \circ }F\] is correct or not.
We shall substitute \[{30^ \circ }C\] in the given relation. If the resultant Fahrenheit is greater than \[{82^ \circ }F\] , then the statement is true, or else the statement will be false.

Complete step by step answer:
Given that \[C = {30^ \circ }C\] and \[{82^ \circ }F\]
To find whether the statement \[{30^ \circ }C\] is higher than \[{82^ \circ }F\] is correct or not.
A relation is given in the question \[5f = 9C + 160\] where \[f\] is the temperature in degrees Fahrenheit \[\left( {^ \circ F} \right)\] and \[C\] is the temperature in degrees Celsius \[\left( {^ \circ C} \right)\] .
We shall substitute \[{30^ \circ }C\] in the given relation.
 \[5f = 9C + 160\]
 \[ \Rightarrow 5f = 9\left( {30} \right) + 160\]
Again after some simplification in the above equation we get,
 \[5f = 270 + 160\]
By adding the above terms we get,
 \[5f = 430\]
Now, dividing it by \[5\] on both sides, we get
 \[f = \dfrac{{430}}{5}\]
Therefore, the value of \[f = {86^ \circ }F\] .
If the resultant Fahrenheit is greater than \[{82^ \circ }F\] , then the statement is true, or else the statement will be false.
Here, \[f = {86^ \circ }F\] is greater than \[{82^ \circ }F\]
Hence, we conclude that the value \[{30^ \circ }C\] is higher than \[{82^ \circ }F\] .
Thus, the statement is correct/true.

Note: If we observe the above calculation in this problem we can able to see that the temperature in degree Celsius \[\left( {^ \circ C} \right)\] is greater than the temperature in degrees Fahrenheit \[\left( {^ \circ F} \right)\] . But in general, it will not hold that the temperature in degrees Celsius \[\left( {^ \circ C} \right)\] is greater than the temperature in degrees Fahrenheit \[\left( {^ \circ F} \right)\] . Hence, we can be better aware of this condition.