Question

The temperature of the water in a swimming pool is \(78^{\circ}\) Fahrenheit. What is the temperature of the water in degrees Celsius? Use the formula \(C=\frac{5}{9}(F-32)\), where \(F\) is the Fahrenheit temperature and \(C\) is the Celsius temperature.

Short answer

The temperature of the water in degrees Celsius is approximately \(25.56^{\circ}\).

Step-by-step solution

Identify given values

In this case, \(F\), the temperature in Fahrenheit is given as 78 degrees.

Apply Fahrenheit to Celsius conversion formula

Substitute the value of Fahrenheit temperature into the conversion formula. \[C=\frac{5}{9}(F-32)\] where \(F = 78^\circ\). Hence, \[C = \frac{5}{9}(78 - 32)\]

Evaluate the formula

Perform the operations inside the parentheses (i.e., subtraction), followed by the division and multiplication. \[C = \frac{5}{9}(46)\] which simplifies to \[C \approx 25.56\]

Key concepts

Understanding Temperature Conversion

Converting temperature from Fahrenheit to Celsius is a common task that requires understanding how these two temperature scales relate to each other. Since Celsius (°C) and Fahrenheit (°F) are used in different parts of the world, being able to switch between them is a useful skill.

The formula for converting Fahrenheit to Celsius is:\(C = \frac{5}{9}(F - 32)\). In this formula, \(C\) represents the temperature in degrees Celsius and \(F\) is the temperature in degrees Fahrenheit. The deductions from 32 and the multiplication by \(\frac{5}{9}\) are based on the differences in the freezing and boiling points of water on both scales. Remember that water freezes at 0°C or 32°F and boils at 100°C or 212°F. This allows us to derive a proportional relationship between the two.

Algebraic Formulas and Their Use

Algebraic formulas are like recipes for mathematics — they provide step-by-step instructions to solve particular kinds of problems. These formulas often include variables and constants. In the context of temperature conversion, the formula \(C = \frac{5}{9}(F - 32)\) is an algebraic formula.

The key to using an algebraic formula is to identify which numbers are constants (always the same in the formula, like the 5, 9, and 32 in our temperature conversion formula) and which are variables (values that change depending on the situation, like \(F\) and \(C\) in our formula). By substituting the known variable values into the formula, you can solve for the unknown variable.

Solving Equations Effectively

When faced with an equation, the goal is to isolate the variable you are solving for on one side of the equation. To achieve this, you'll follow a series of steps that might include adding, subtracting, multiplying, or dividing both sides of the equation by the same number or expression. In the case of our Fahrenheit to Celsius conversion:
By plugging the value of 78°F into the formula for \(F\), we simplify within the parentheses first, following the order of operations (often remembered by the acronym PEMDAS - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). After simplifying the subtraction, we then multiply the result by \(\frac{5}{9}\) to find the temperature in Celsius.

Learning to follow these steps reliably and perform the necessary arithmetic is essential for solving equations effectively in algebra.