Question

The temperature increased 12 degrees between 9 AM and noon. It decreased 9 degrees Fahrenheit between between noon and 6 PM. Write an expression with three terms to show the change in temperature. Let the first term represent the temperature at 9AM. If the temperature was 45 degrees Fahrenheit at 9 AM what was the temperature at 6 PM? Suppose to the temperature at 6 PM was 30 degrees Fahrenheit. What would the temperature have been at 9 AM? Explain how you can use the expression you wrote in problem 4 to find the answer.

Answer 1

Let x be the temperature at 9 AM. It increased 12°F until noon and then decreased 9°F until 6 PM.

The temperature at 6 PM can be calculated by:

x + 12 - 9

That is the required 3-term expression.

It can be used to calculate the temperature at 6 PM if we know the temperature at 9 AM was x = 45°F. Substituting:

45 + 12 - 9 = 48

The temperature at 6 PM was 48°F

Now we are given the temperature at 6 PM as 30°F. It's required to find the initial temperature at 9 AM. We write the equation:

x + 12 - 9 = 30

Operating:

x + 3 = 30

Subtracting 3:

x = 27°F

The temperature was 27°F at 9 AM

We used the expression to solve an equation that gave us the value of x