Question
The formula \( F=32+\frac{9 C}{5} \quad \) is used for converting temperatures for degrees Celsius ( \( { }^{\circ} C \) ) to degrees Fahrenheit ( \( { }^{\circ} F \) ). Make \( C \) the subject of this formula.
Ask by Joseph Tran. in South Africa
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( C = \frac{5F - 160}{9} \)
Solution
Solve the equation \( 5F=9C+160 \).
Solve the equation by following steps:
- step0: Solve for \(C\):
\(5F=9C+160\)
- step1: Swap the sides:
\(9C+160=5F\)
- step2: Move the constant to the right side:
\(9C=5F-160\)
- step3: Divide both sides:
\(\frac{9C}{9}=\frac{5F-160}{9}\)
- step4: Divide the numbers:
\(C=\frac{5F-160}{9}\)
The formula \( F=32+\frac{9C}{5} \) can be rewritten with \( C \) as the subject as follows:
\[ C = \frac{5F-160}{9} \]
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Simplify this solution The Deep Dive
To make \( C \) the subject of the formula \( F=32+\frac{9 C}{5} \), we start by isolating the term containing \( C \). 1. Subtract 32 from both sides: \[ F - 32 = \frac{9 C}{5} \] 2. Multiply both sides by 5 to eliminate the fraction: \[ 5(F - 32) = 9C \] 3. Finally, divide both sides by 9 to solve for \( C \): \[ C = \frac{5(F - 32)}{9} \] So, the formula for converting Fahrenheit back to Celsius is \( C = \frac{5(F - 32)}{9} \).
