Problem 123 - Beginning and Intermediate Algebra

Question

Solve each problem. The lowest temperature ever recorded in Arkansas was \(-29^{\circ} \mathrm{F}\). The highest temperature ever recorded there was \(149^{\circ} \mathrm{F}\) more than the lowest. What was this highest temperature? (Data from National Climatic Data Center.)

Step-by-Step Solution

Answer

The highest temperature recorded was 120°F.

Step 1 - Understand the variables

Identify the lowest temperature, which is \( -29^{\c} \mathrm{F} \), and the increase from this temperature, which is \( 149^{\circ} \mathrm{F} \).

Step 2 - Set up the equation

To find the highest temperature, set up the equation: Highest Temperature = Lowest Temperature + Increase.

Step 3 - Substitute and solve

Substitute the known values into the equation: \( \text{Highest Temperature} = -29 + 149 \). Calculate the sum: \( -29 + 149 = 120 \).

Step 4 - Verify the result

Check the calculation to ensure there are no errors: \( -29 + 149 = 120 \). Therefore, the highest temperature recorded is accurate.

Key Concepts

Temperature Calculations

Understanding temperature calculations is crucial in many everyday situations and scientific contexts. In this exercise, we need to find the highest temperature ever recorded in Arkansas based on the given lowest temperature and the increase from that temperature.
To start, let's identify the values given in the problem:

• Lowest Temperature: \( -29^{\circ} \mathrm{F} \)
• Increase from the Lowest Temperature: \( 149^{\circ} \mathrm{F} \)

Now, the formula we use to find the highest temperature is:
\[ \text{Highest Temperature} = \text{Lowest Temperature} + \text{Increase} \]
By substituting the known values into this equation and performing simple arithmetic, we can solve for the highest temperature. Make sure to double-check your work to ensure accuracy.

Simple Arithmetic

Arithmetic is the foundation of all mathematics. It includes basic operations like addition, subtraction, multiplication, and division. Here, we are focused on addition and subtraction.
Given our problem, we need to solve:
\[ -29 + 149 \]
It's important to remember how addition with negative numbers works. Think of \( -29 \) as owing 29 units and \( +149 \) as gaining 149 units. If you gain more than you owe, you are left with the difference as a positive number. So,

\[ 149 - 29 = 120 \]
This calculation shows that the highest temperature is thus \( 120^{\circ} \mathrm{F} \). Simple arithmetic is essential in solving many such everyday problems.

Variables in Algebra

Variables are symbols used to represent unknown values or values that can change. They are fundamental in algebra and help us form equations that model real-world problems.
In this exercise, variables help structure the problem efficiently. We can set:

• \( \text{Lowest Temperature} = -29^{\circ} \mathrm{F} \)
• \( \text{Increase} = 149^{\circ} \mathrm{F} \)
• \( \text{Highest Temperature} = \text{Lowest Temperature} + \text{Increase} \)

By substituting the variables with known values, we simplify our calculation:

• \( \text{Highest Temperature} = -29 + 149 \)
• \( \text{Highest Temperature} = 120^{\circ} \mathrm{F} \)

Understanding and using variables in algebra allows us to generalize and solve problems more systematically and effectively.