Problem 102 - Intermediate Algebra

Question

Write a numerical statement to represent the problem. Then simplify the numerical expression to answer the 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: Initial Temperature Representation

First, let's consider the initial temperature of the afternoon in Florida, which is given as \(96^{\circ} \mathrm{F}\). This is our starting point for the numerical expression.

Step 2: Represent Temperature Change After the Thunderstorm

The problem states that after the thunderstorm, the temperature dropped by \(8^{\circ} \mathrm{F}\). We represent this change by subtracting 8 from the initial temperature. Thus, the expression becomes \(96 - 8\).

Step 3: Calculate the Temperature After the Thunderstorm

Simplify the expression from Step 2 to find the temperature after the storm. Calculate \(96 - 8 = 88^{\circ} \mathrm{F}\). This is the temperature immediately after the thunderstorm.

Step 4: Represent Temperature Rise After Sun Returns

The problem states that when the sun comes back, the temperature rises by \(5^{\circ} \mathrm{F}\). Add 5 to the temperature after the storm. The expression is now \(88 + 5\).

Step 5: Calculate the Final Temperature

Simplify the expression from Step 4 to find the final temperature. Calculate \(88 + 5 = 93^{\circ} \mathrm{F}\). This is the final temperature after the sun comes back out.

Key Concepts

Understanding Temperature Changes

Understanding temperature changes helps us grasp how weather can fluctuate throughout the day. In this exercise, we start with an afternoon temperature of \(96^{\circ} \mathrm{F}\). After a thunderstorm, it drops by \(8^{\circ} \mathrm{F}\), showcasing how quickly weather events can impact temperature.
The subsequent rise of \(5^{\circ} \mathrm{F}\) when the sun re-emerges is another common occurrence. Such variations can be quite typical in areas like Florida, where thunderstorms are frequent. Understanding these changes in temperature isn't just about arithmetic—it connects to recognizing weather patterns and their effects on our environment. By analyzing these temperature shifts, students can understand the relationship between weather events and daily temperature trends.

Simple Arithmetic Operations Simplified

Simple arithmetic operations are the building blocks of mathematics. They include addition, subtraction, multiplication, and division. In this problem, we use addition and subtraction to solve the temperature changes.

• Subtraction: The afternoon temperature decreases, so we subtract \(8^{\circ} \mathrm{F}\) from \(96^{\circ} \mathrm{F}\).
• Addition: When the sun returns, the temperature increases, so we add \(5^{\circ} \mathrm{F}\) to the new temperature of \(88^{\circ} \mathrm{F}\).

This is a good example of how simple operations can be applied to real-world scenarios. It's about breaking down the problem into small, manageable parts, where each number in the arithmetic expression has a specific meaning in the context of temperature change.

Following Problem-Solving Steps

Problem-solving steps provide a structured way to tackle complex problems, making them more manageable. Here's a breakdown based on this exercise:

• Step 1: Identify the starting condition. Here, the temperature is initially \(96^{\circ} \mathrm{F}\).
• Step 2: Understand and represent the first change. Subtract \(8^{\circ} \mathrm{F}\) due to the thunderstorm.
• Step 3: Calculate the result of the first change to get \(88^{\circ} \mathrm{F}\).
• Step 4: Represent the additional change. Add \(5^{\circ} \mathrm{F}\) for when the sun comes out again.
• Step 5: Calculate the final temperature, resulting in \(93^{\circ} \mathrm{F}\).

This approach helps in logically organizing thoughts and calculations, ensuring every aspect of the problem is addressed comprehensively. By sequentially following these steps, students can solve similar problems independently with confidence.