A solution is to be kept between 86^ and 95^ F. What is the range… - Vidyadip

Question

A solution is to be kept between $86^\circ $ and $95^\circ F$. What is the range of temperature in degree Celsius, if the Celsius (C)/ Fahrenheit (F) conversion formula is given by $\text{F}=\frac{9}{5}\text{C}+32.$

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Answer

We have,
$F_1 = 86^\circ F$
$\therefore\text{F}_1=\frac{9}{5}\text{C}_1+32$ $\Big[\because\text{F}=\frac{9}{5}\text{C}+32\Big]$
$\Rightarrow86=\frac{9}{5}\text{C}_1+32$
$\Rightarrow86-32=\frac{9}{5}\text{C}_1$
$\Rightarrow54=\frac{9}{5}\text{C}_1$
$\Rightarrow9\text{C}_1=5\times54$
$\Rightarrow\text{C}_1=\frac{5\times54}{9}$
$\Rightarrow\text{C}_1=5\times6=30^\circ\text{C}$
Now, $\text{F}_2=95^\circ\text{F}$
$\therefore\text{F}_2=\frac{9}{5}\text{C}_2+32$
$\Rightarrow95-32=\frac{9}{5}\text{C}_2$
$\Rightarrow63=\frac{9}{5}\text{C}_2$
$\Rightarrow9\text{C}_2=63\times5$
$\Rightarrow\text{C}_2=\frac{63\times5}{9}$
$\Rightarrow\text{C}_2=7\times5=35^\circ\text{C}$
The range of temperature of the solution is from $30^\circ C$ to $35^\circ C$.

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