Explanation:

The temperature at which the readings on the Celsius and Fahrenheit scales are the same is -40 degrees. To understand why, let's examine the relationship between the two scales.

The Fahrenheit (°F) and Celsius (°C) scales differ in their zero points and the size of their degree intervals. The formula to convert between them is:

°F = (°C × 9/5) + 32

Now, when the readings are the same on both scales, we have:

°F = °C

Substitute this into the conversion formula:

°F = (°F × 9/5) + 32

Now, solve for °F:

°F = °F × 9/5 + 32

Subtract °F from both sides:

0 = °F × 9/5 + 32 - °F

Now, isolate °F:

°F × 9/5 - °F = -32

Combine like terms:

°F (9/5 - 1) = -32

Simplify:

°F (4/5) = -32

Now, divide both sides by 4/5:

°F = (-32) / (4/5) = -32 ÷ (4/5)

To divide by a fraction, multiply by its reciprocal:

°F = -32 * (5/4) = -40

So, at -40 degrees, the readings on the Celsius and Fahrenheit scales are the same ..