Problem 98 - Algebra for College Students

Question

On a summer day in Florida, the afternoon temperature was \(96^{\circ} \mathrm{F}\). After a thunderstorm, the temperature dropped \(8^{\circ} \mathrm{F}\). What would be the temperature if the sun came back out and the temperature rose \(5^{\circ} \mathrm{F}\) ?

Step-by-Step Solution

Answer

The final temperature is \(93^{\circ} \mathrm{F}\).

Step 1: Identify the Initial Temperature

The initial temperature before any changes is given as \(96^{\circ} \mathrm{F}\).

Step 2: Calculate Temperature After Drop

The temperature drops by \(8^{\circ} \mathrm{F}\) after the thunderstorm. Subtract this value from the initial temperature: \[ 96^{\circ} \mathrm{F} - 8^{\circ} \mathrm{F} = 88^{\circ} \mathrm{F} \] Thus, the temperature is \(88^{\circ} \mathrm{F}\) after the drop.

Step 3: Calculate Final Temperature After Rise

The temperature rises by \(5^{\circ} \mathrm{F}\) when the sun comes back. Add this value to the temperature after the drop: \[ 88^{\circ} \mathrm{F} + 5^{\circ} \mathrm{F} = 93^{\circ} \mathrm{F} \] Thus, the final temperature is \(93^{\circ} \mathrm{F}\).

Key Concepts

Understanding Initial Temperature

The initial temperature is simply the temperature at the starting point of our observations. In this specific scenario, the initial temperature is taken before any weather changes, such as a thunderstorm, have influenced it. Knowing the initial temperature is crucial, as it serves as a reference point for calculating any changes that follow.
In the given exercise, the initial temperature is clearly stated as \(96^{\circ} \mathrm{F}\). This value is the baseline from which all subsequent temperature changes are measured. To manage problems involving temperature changes effectively, always start by identifying the initial temperature. Without this step, any further calculations may be inaccurate or misleading.

Calculating Temperature Drop

A temperature drop refers to a decrease in temperature, often caused by weather events, like in this case, a thunderstorm. The calculation of a temperature drop requires a simple subtraction of the drop value from the initial temperature.
For example:

• Start with the initial temperature, which is \(96^{\circ} \mathrm{F}\).
• The temperature drop due to the thunderstorm is \(8^{\circ} \mathrm{F}\).
• Subtract this from the initial temperature: \(96^{\circ} \mathrm{F} - 8^{\circ} \mathrm{F} = 88^{\circ} \mathrm{F}\).

It's as simple as that! The resulting \(88^{\circ} \mathrm{F}\) is the new temperature after the thunderstorm has taken effect. This process highlights the direct nature of managing temperature drops in problems like this one.

Understanding Temperature Rise Calculation

A temperature rise calculation is quite similar to calculating a drop, but this time, you add a value instead of subtracting it. It's important to apply this operation to the temperature recorded after any prior changes. For instance, after a thunderstorm, when the skies clear, the temperature often increases.
Here’s how you calculate it:

• Take the temperature after the drop, which is \(88^{\circ} \mathrm{F}\).
• Add the temperature rise caused by the sun returning, which is \(5^{\circ} \mathrm{F}\).
• This gives us: \(88^{\circ} \mathrm{F} + 5^{\circ} \mathrm{F} = 93^{\circ} \mathrm{F}\).

The new temperature of \(93^{\circ} \mathrm{F}\) represents the final result after accounting for both the drop and rise in temperature. This basic addition encapsulates how temperature naturally fluctuates in response to environmental changes.