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Math Help - Inequalities question

  1. #1
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    Inequalities question

    1) A city commission has propsed two tax bills. The first bill requires that a homeowner pay $1800 plus 3% of the assessed home value in taxes. The second bill requres taxes of $200 plus 8% of the assessed home value. What price range of home assessment would make the first bill a better deal?
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  2. #2
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    Quote Originally Posted by lemontea View Post
    1) A city commission has propsed two tax bills. The first bill (A) requires that a homeowner pay $1800 plus 3% of the assessed home value in taxes. The second bill (B) requres taxes of $200 plus 8% of the assessed home value. What price range of home assessment would make the first bill a better deal?
    Hello,

    let v be the value of the home
    and the tax to be payed.

    Then you have:

    (A): t(v) = 1800+0.03 \cdot v

    (B): t(v) = 200 + 0.08 \cdot v

    The graphs of these equations are straight lines. Calculate the intersection. The coordinates of the intersection are the value of the home which will cause the same tax no matter which bill you choose.

    I've got v = 32,000 $ and t = 2,760 $

    Because the slope of (B) is greater than the slope of (A) the 2nd bill will be much more expensive if v > 32,000 $. Thus (A) is better if the value of the house is greater than 32,000 $
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