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Math Help - Converting Farenheit to Arbitrary Scale

  1. #1
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    Converting Farenheit to Arbitrary Scale

    Suppose you have designed a new thermometer called the X thermometer. On the X scale the boiling point of water is 121 and the freezing point of water is 20.
    At what temperature will the readings on the Fahrenheit and X thermometers be the same?




    trying to mess with slopes but I'm coming up short. any help?
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by coolguy99 View Post
    Suppose you have designed a new thermometer called the X thermometer. On the X scale the boiling point of water is 121 and the freezing point of water is 20.
    At what temperature will the readings on the Fahrenheit and X thermometers be the same?




    trying to mess with slopes but I'm coming up short. any help?
    to fiend a formula for converting between F to X

    at Fahrenheit the water boiling at 212 and freeze at 32 and in X 121 and 20 for freeze

    \frac{F-32}{212-32} = \frac{X-20}{121-20}

    \frac{F-32}{180}=\frac{X-20}{101}

    you want the temperature where F=X sub X=F

    \frac{F-32}{180}=\frac{F-20}{101}


    find F value .....
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  3. #3
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    Quote Originally Posted by coolguy99 View Post
    Suppose you have designed a new thermometer called the X thermometer. On the X scale the boiling point of water is 121 and the freezing point of water is 20.
    At what temperature will the readings on the Fahrenheit and X thermometers be the same?

    trying to mess with slopes but I'm coming up short. any help?
    Amer has the math.

    To help understand:
    plot the two points: X along the x-axis, and F along the y-axis.

    Along the x-axis at x=20, plot y=32
    & at x=121, y=212

    You can scale off the values (in either direction).
    That will assist in finding the "slope" and intercept.
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