Final answer:
To find the original Celsius reading of -x from an incorrect reading that was taken as x °F, which coincidentally was the correct Fahrenheit temperature, we use the temperature conversion formula (F = (C × 9/5) + 32). By solving the equation, we determine that the original Celsius temperature was -11.4 °C.
Step-by-step explanation:
The question asks for the original Celsius temperature if a freezer temperature read incorrectly as positive and then as Fahrenheit was still the correct Fahrenheit value. To solve this problem, we use the temperature conversion formula between Celsius (C) and Fahrenheit (F): F = (C × 9/5) + 32. In this scenario, the erroneously read temperature in Fahrenheit is actually the true temperature in Fahrenheit.
We know that the original Celsius temperature is negative and let's call it -x. The incorrect reading removed the negative, so we have x, and then the individual thought it was in Fahrenheit, so the read value is also x (as in x °F). Plugging this into the temperature conversion formula, we get x = (-x × 9/5) + 32.
To find x, we solve the equation: x = (-x × 9/5) + 32. Combining like terms and solving for x gives us the original Celsius reading: x × (1 + 9/5) = 32, and x × 14/5 = 32, which simplifies to x = (32 × 5/14). So, we get x = 11.4286. Rounding to three significant figures gives us -11.4 °C as the original Celsius temperature.