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Question

Calculate the temperature at which the value in degrees celsius and degrees Fahernheit is same.

Solution
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The relationship between $$)^{\circ}0 $$ and $$ ^{\circ}F $$ is:

$$ ^{\circ}C = \dfrac{5}{9} (F - 32) $$

If $$ x ^{\circ}C = x ^{\circ}F, $$ then $$ x = \dfrac{5}{9}(x - 32) $$

or $$ 9x = 5x - 160 $$ or $$ 4x = - 160 $$

or $$ x = - 40^{\circ}C $$

Thus $$ - 40^{\circ}C = - 40^{\circ}F.$$

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