At what temperature on the Fahrenheit scale will the reading be double of the reading on the Celsius scale?

Explanation

To solve the problem of finding the temperature on the Fahrenheit scale where the reading is double that of the Celsius scale, we can follow these steps:

### Step 1: Understand the relationship between Celsius and Fahrenheit
The formula to convert Celsius (C) to Fahrenheit (F) is given by:
\[ F = \frac{9}{5}C + 32 \]

### Step 2: Set up the equation based on the problem statement
According to the problem, we want the Fahrenheit reading to be double the Celsius reading. This can be expressed as:
\[ F = 2C \]

### Step 3: Substitute the expression for F into the equation
Now, we can substitute \( F \) from the second equation into the first equation:
\[ 2C = \frac{9}{5}C + 32 \]

### Step 4: Solve for C
To solve for \( C \), first, we can eliminate the fraction by multiplying the entire equation by 5:
\[ 10C = 9C + 160 \]

Next, we can isolate \( C \) by subtracting \( 9C \) from both sides:
\[ 10C - 9C = 160 \]
\[ C = 160 \]

### Step 5: Find the corresponding Fahrenheit temperature
Now that we have \( C = 160 \), we can find the corresponding Fahrenheit temperature using the conversion formula:
\[ F = \frac{9}{5} \times 160 + 32 \]
\[ F = 288 + 32 \]
\[ F = 320 \]

### Conclusion
Thus, the temperature on the Fahrenheit scale at which the reading is double that of the Celsius scale is:
**320°F**.

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