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The Celsius scale of temperature can be converted to Fahrenheit scale using the relationship $$F = 1.8C + 32$$, where $$F$$ and $$C$$ are temperature recorded in degrees Fahrenheit and Celsius, respectively. Ajay noted down the temperature of a chemical reaction as $$x$$ degrees Fahrenheit but reported it as $$x$$ degrees Celsius by mistake. If this led to a recording of the temperature that was 144% higher than the actual temperature in Celsius scale, then $$x$$ equals ____
Correct Answer: 122
$$F = 1.8C + 32$$. Actual temperature is $$x°F$$, but Ajay wrote it as $$x°C$$. The actual value in Celsius is $$\dfrac{x-32}{1.8}$$. The recorded value ($$x$$ Celsius) is 144% higher than the actual Celsius value:
$$x = 2.44 \cdot \dfrac{x-32}{1.8} \Rightarrow 1.8x = 2.44(x-32) \Rightarrow 1.8x = 2.44x - 78.08 \Rightarrow 0.64x = 78.08 \Rightarrow x = 122$$.
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