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Question
A solution is to be kept between 86° and 95°F. What is the range of temperature in degree Celsius, if the Celsius (C)/ Fahrenheit (F) conversion formula is given by\[F = \frac{9}{5}C + 32\]
Solution
Suppose the temperature of the solution is x degree Celsius.
∴ x in Fahrenheit = \[\frac{9}{5}x + 32\]
Then, as per the given condition:
\[86 < \frac{9}{5}x + 32 < 95\]
\[ \Rightarrow 86 - 32 < \frac{9}{5}x < 95 - 32 (\text{ Subtratcting 32 throughout })\]
\[ \Rightarrow 54 < \frac{9}{5}x < 63\]
\[ \Rightarrow \frac{5}{9} \times 54 < \frac{5}{9} \times \frac{9}{5}x < \frac{5}{9} \times 63 (\text{ Multiplying by } \frac{5}{9} \text{ throughout })\]
\[ \Rightarrow 30 < x < 35\]
Hence, the range of the temperature in degree Celsius is between 30° C and 35° C
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