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The Celsius scale of temperature can be converted to Fahrenheit scale using the relationship F=1.8C+32F = 1.8C + 32, where FF and CC are temperature recorded in degrees Fahrenheit and Celsius, respectively. Ajay noted down the temperature of a chemical reaction as xx degrees Fahrenheit but reported it as xx 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 xx equals ___

Entered answer:

Solution

Correct Answer: 122

The actual temperature was xx °F.

Converting to Celsius using F=1.8C+32F = 1.8C + 32:

C=x321.8C = \dfrac{x - 32}{1.8}

This is the actual temperature in Celsius.


Ajay mistakenly reported the temperature as xx °C instead of xx °F.

The reported value is 144% higher than the actual Celsius value, meaning the reported value is 244%244\% of the actual value (100%+144%=244%)(100\% + 144\% = 244\%).

x=2.44×x321.8x = 2.44 \times \dfrac{x - 32}{1.8}


Multiply both sides by 1.81.8:

1.8x=2.44(x32)1.8x = 2.44(x - 32)

1.8x=2.44x78.081.8x = 2.44x - 78.08

1.8x2.44x=78.081.8x - 2.44x = -78.08

0.64x=78.08-0.64x = -78.08

x=78.080.64x = \dfrac{78.08}{0.64}

x=122x = 122


Verification:

Actual temperature =122= 122 °F =122321.8=901.8=50= \dfrac{122 - 32}{1.8} = \dfrac{90}{1.8} = 50 °C

Reported temperature =122= 122 °C

Percentage higher =1225050×100=144%= \dfrac{122 - 50}{50} \times 100 = 144\%


x=122x = 122

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