Problem 125 - Beginning and Intermediate Algebra

Question

Solve each problem. The lowest temperature ever recorded in Illinois was \(-36^{\circ} \mathrm{F}\) on January \(5,1999 .\) The lowest temperature ever recorded in Utah was on February \(1,1985,\) and was \(33^{\circ} \mathrm{F}\) lower than Illinois's record low. What is the record low temperature for Utah? (Data from National Climatic Data Center.)

Step-by-Step Solution

Answer

The record low temperature for Utah is -69°F.

Step 1 - Understand the problem

We need to find the lowest recorded temperature in Utah, which is given as 33 degrees Fahrenheit lower than the lowest recorded temperature in Illinois (-36°F).

Step 2 - Set up the equation

To find Utah's record low, we need to subtract 33°F from Illinois's record low. This can be expressed as: \[ \text{Utah's record low} = \text{Illinois's record low} - 33^{\bullet} \text{F} \]

Step 3 - Substitute the given value

Substitute Illinois's record low (-36^{\bullet}F) into the equation: \[ \text{Utah's record low} = -36^{\bullet}F - 33^{\bullet}F \]

Step 4 - Calculate the result

Perform the subtraction: \[ -36 - 33 = -69 \] So, the lowest temperature ever recorded in Utah is -69°F.

Key Concepts

temperature comparison

Understanding how to compare temperatures, especially temperatures that are below zero, is crucial in this exercise. When we talk about one temperature being a certain number of degrees lower than another, we need to subtract that number from the given temperature. In this case, the temperature in Utah is described as 33 degrees Fahrenheit lower than the record low in Illinois.

When dealing with temperatures, it's important to note the signs. Temperatures above zero are positive, and temperatures below zero are negative. This can affect the calculations, as subtracting a positive number from a negative number will result in a more negative number.

negative numbers

Negative numbers are numbers less than zero. They appear often in real-life scenarios like temperature readings, bank balances, and elevations below sea level. A negative number can be thought of as being in the opposite direction of a positive number on a number line.

In this problem, we're working with negative numbers to describe very low temperatures. The record low temperature in Illinois is -36°F, which is 36 degrees below zero. To find a temperature that is lower than another, we subtract a positive number from a negative number, leading to a more negative result.

subtraction in algebra

In algebra, subtraction is used to find the difference between two values. Here, the value we need to subtract is 33°F from Illinois's record low of -36°F. The subtraction operation in algebra remains consistent, whether we are dealing with positive or negative numbers.

The correct equation reflecting this problem is: Utah's record low = Illinois's record low - 33°F.

We substitute -36°F for Illinois’s record low, yielding the equation:-36 - 33 = -69.
This subtraction results in -69°F, indicating that Utah's record low temperature is significantly lower than that of Illinois.