Question

The temperature in the morning is \[88.3^\circ F\] and it increases to \[103.8^\circ F\] by afternoon. What is the increase in temperature?

Answer 1

Hint: Here, we need to find the increase in temperature. We will assume the increase in temperature be \[x^\circ F\]. We will use the given information to obtain an equation in terms of \[x\]. Then, we will solve this equation to find the value of \[x\] and hence, find the required increase in temperature.

Complete step-by-step answer:
Let the increase in temperature be \[x^\circ F\].
We will use the given information to form an equation in terms of \[x\].
We know that the sum of the temperature in the morning and the required increase in temperature, is equal to the temperature in the afternoon.
Thus, we will add the temperature in the morning and the required increase in temperature.
Adding \[88.3^\circ F\] and \[x^\circ F\], we get the expression
\[88.3^\circ F + x^\circ F\]
Now, it is given that the temperature in the afternoon is \[103.8^\circ F\].
Thus, we get the equation
\[88.3^\circ F + x^\circ F = 103.8^\circ F\]
We need to solve this equation to get the value of \[x\] and hence, find the increase in temperature.
Subtracting \[88.3^\circ F\] from both sides of the equation, we get
\[ \Rightarrow 88.3^\circ F + x^\circ F - 88.3^\circ F = 103.8^\circ F - 88.3^\circ F\]
\[ \Rightarrow x^\circ F = 15.5^\circ F\]
Thus, we get the value of \[x^\circ F\] as \[15.5^\circ F\].
\[\therefore\] We get the increase in temperature as \[15.5^\circ F\].

Note: We have formed a linear equation in one variable from the given information in this question. A linear equation in one variable is an equation of the form \[ax + b = 0\], where \[a\] and \[b\] are integers. A linear equation of the form \[ax + b = 0\] has only one solution.
We can also verify our answer by using the given information.
The sum of the temperature in the morning and the required increase in temperature, is equal to the temperature in the afternoon.
Adding \[88.3^\circ F\] and \[15.5^\circ F\], we get \[88.3^\circ F + 15.5^\circ F = 103.8^\circ F\].
Thus, if the temperature in the morning is increased by \[15.5^\circ F\], then the temperature in the afternoon is \[103.8^\circ F\].
Hence, we have verified our answer.