Joanna Mueller

2022-07-18

Water boils as 100C(derees Celsius) which is 212F(degrees Fahrenheit) and freezes at 0C which is 32 F.Let x denote the temperature of an object in: F and y the temperature of the same object in: C
(a) Express x in terms of y (F)
(b) Express y in terms of y (C)
(c) Use (b) to convert 70 F into Celsius
(d) Use (a) to convert your answer to (c) back into Fahrenheit.
(e) What temperature is the same in both Celsius and Fahrenheit?

sweetwisdomgw

Expert

Let $x=ay+b$
When
When
(1) $⇒212=100a+32⇒a=\frac{212-32}{100}\phantom{\rule{0ex}{0ex}}⇒a=\frac{180}{100}=\frac{9}{5}\phantom{\rule{0ex}{0ex}}\therefore x\left(y\right)=\frac{9}{5}y+32$
a) $x\left(y\right)=\frac{9}{5}y+32F$
b) $\therefore \frac{9}{5}y=x-32⇒y=\frac{5}{9}\left(x-32\right)\phantom{\rule{0ex}{0ex}}⇒y\left(x\right)=\frac{5x}{9}-\frac{160}{9}C$
c) When $x=70F,y=\frac{5\left(70\right)}{9}-\frac{160}{9}\phantom{\rule{0ex}{0ex}}⇒y=\frac{350-160}{9}=\frac{190}{9}C$
d) $x=\frac{9}{5}\left(\frac{190}{9}\right)+32\phantom{\rule{0ex}{0ex}}=\frac{190}{5}+32=\frac{190+160}{5}=\frac{350}{5}=70F$
e) When x=y, from (a), $x=\frac{9}{5}$
$⇒x-\frac{9}{5}x=32⇒\frac{-4}{5}x=32\phantom{\rule{0ex}{0ex}}⇒x=\frac{32×-5}{4}=-40C=-40F$

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