Answer to Question #120046 in Molecular Physics | Thermodynamics for Meryclare

Question

At what temperature on the Fahrenheit scale will the temperature on a centigrade scale be
three times that on a Fahrenheit scale?

Answer 1

We know that the Fahrenheit scale can be converted to the centigrade scale as

$t(^\circ\mathrm{C}) = (t(^\circ\mathrm{F}) - 32)\cdot 5/9.$

$t(^\circ\mathrm{C})$ should be equal to $3t(^\circ\mathrm{F})$ , therefore we obtain an equation

$3t(^\circ\mathrm{F}) = (t(^\circ\mathrm{F}) - 32)\cdot 5/9.$

$27t(^\circ\mathrm{F}) = 5t(^\circ\mathrm{F})-160, \;\; t(^\circ\mathrm{F}) = -7\dfrac{3}{11}^\circ F \approx-7.3^\circ F.$