Question

What is the temperature in degrees Celsius if the temperature in degrees Fahrenheit is \(95^{\circ} \mathrm{F}\) ? The temperature conversion formula is $$ F=\frac{9}{5} C+32 $$ A. 35 B. 39 C. 41 D. 63

Short answer

35°C

Step-by-step solution

Identify the given temperature in Fahrenheit

The given temperature is 95°F. Note this value as it will be used in the formula for conversion.

Write down the temperature conversion formula

The formula for converting Fahrenheit to Celsius is: \[ F = \frac{9}{5}C + 32 \] We'll use this formula to solve for the temperature in degrees Celsius (C).

Substitute the given Fahrenheit value into the formula

Replace F with 95 in the formula: \[ 95 = \frac{9}{5}C + 32 \] This gives us an equation to solve for C.

Isolate the term involving C

Subtract 32 from both sides of the equation to isolate the term involving C: \[ 95 - 32 = \frac{9}{5}C \] Simplify the left side: \[ 63 = \frac{9}{5}C \]

Solve for C

To solve for C, multiply both sides of the equation by \( \frac{5}{9} \) to cancel out the fraction: \[ C = 63 \times \frac{5}{9} \] Calculate the result: \[ C = 35 \]

Verify the calculated temperature in Celsius

Double-check the calculation. By substituting 35 back into the formula, we can confirm the correctness of our result: \[ F = \frac{9}{5} \times 35 + 32 = 95 \]

Key concepts

Fahrenheit to Celsius

Temperature conversion between Fahrenheit and Celsius is a useful skill when interpreting weather reports, engaging in scientific experiments, or traveling to countries using different temperature scales. The Fahrenheit scale is commonly used in the United States, while most other countries use the Celsius scale. Understanding the conversion process helps you accurately interpret temperature readings no matter the scale used. Here's a simple example to illustrate this process. We are given a temperature of 95 degrees Fahrenheit and need to convert it to Celsius. Using the necessary formula and some basic algebra, we can complete this conversion efficiently.

Conversion Formula

The key to converting Fahrenheit to Celsius is using the proper conversion formula. The specific formula used for this conversion is: \[ F = \frac{9}{5}C + 32 \] where \( F \) represents degrees Fahrenheit, and \( C \) represents degrees Celsius. This formula allows us to substitute the known temperature in Fahrenheit and solve for the corresponding temperature in Celsius. The formula essentially states that to convert Celsius to Fahrenheit, you multiply the Celsius temperature by \( \frac{9}{5} \), and then add 32. For our specific example, we need to find the Celsius equivalent of 95°F. To do this, we'll rearrange the formula to solve for \( C \).

Solving Equations

Solving equations is a fundamental skill in algebra and is used to isolate and find the value of a specific variable. In our case, we need to solve for \( C \) in the equation: \[ 95 = \frac{9}{5}C + 32 \] To begin, isolate the term involving \( C \) by subtracting 32 from both sides of the equation: \[ 95 - 32 = \frac{9}{5}C \] Simplify to get: \[ 63 = \frac{9}{5}C \] Next, to solve for \( C \), multiply both sides by the reciprocal of \( \frac{9}{5} \), which is \( \frac{5}{9} \): \[ C = 63 \times \frac{5}{9} \] Calculate the product: \[ C = 35 \] This means that 95°F is equivalent to 35°C. Verifying your answer by substituting it back into the original formula ensures accuracy and understanding of the conversion process.