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Math Help - Circular mirrors are expensive

  1. #1
    Member GAdams's Avatar
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    Circular mirrors are expensive

    The cost of a circular mirror is directly proportional to the square of the diameter.
    A circular mirror with a diameter of 6cm costs $50.

    What is the cost of a circular mirror with a diameter of 90 cm?


    This is what I tried:
    If a 60cm mirror costs $50, then each cm is 50/60 = 0.83 per cm. Therefore, 90 * 0.83 = 75 cm. But this is wrong. Help.



    PS how do I put up a graph question here? There doesn't seem to be a copy an attach or copy & paste function.
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  2. #2
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by GAdams View Post
    The cost of a circular mirror is directly proportional to the square of the diameter.
    A circular mirror with a diameter of 6cm costs $50.

    What is the cost of a circular mirror with a diameter of 90 cm?


    This is what I tried:
    If a 60cm mirror costs $50, then each cm is 50/60 = 0.83 per cm. Therefore, 90 * 0.83 = 75 cm. But this is wrong. Help.



    PS how do I put up a graph question here? There doesn't seem to be a copy an attach or copy & paste function.
    This is how you set up a proportional problem. The letter "k" represents the constant of proportionality.

    C=kD^2

    Since we have that a 60cm mirror costs $50, we can find "k" as:

    50 = k(60)^2
    \Rightarrow k=50/3600=5/360=1/72

    Now we need to find the cost of a 90 cm mirror:

    C= \frac {1}{72}(90)^2 = \frac {1}{72}(8100) = \$112.50
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