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?

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sweetwisdomgw · Accepted Answer

Let   x  =  a  y  +  bWhen   x  =      212    ∘    F  ,  y  =  100    ∴  212  =  100  a  +  b              (  1  )When   x  =      212    ∘    F  ,  y  =  100    ∴  212  =  100  a  +  b              (  1  )(1)   ⇒  212  =  100  a  +  32  ⇒  a  =            212      −      32        100      ⇒  a  =      180    100    =      9    5      ∴  x  (  y  )  =      9    5    y  +  32a)   x  (  y  )  =      9    5    y  +  32  Fb)   ∴      9    5    y  =  x  −  32  ⇒  y  =      5    9    (  x  −  32  )    ⇒  y  (  x  )  =            5      x        9    −      160    9    Cc) When   x  =  70  F  ,  y  =            5      (      70      )        9    −      160    9      ⇒  y  =            350      −      160        9    =      190    9    Cd)   x  =      9    5    (      190    9    )  +  32    =      190    5    +  32  =            190      +      160        5    =      350    5    =  70  Fe) When x=y, from (a),   x  =      9    5    ⇒  x  −      9    5    x  =  32  ⇒            −      4        5    x  =  32    ⇒  x  =            32      ×      −      5        4    =  −  40  C  =  −  40  F

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