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Math Help - inequality word problem

  1. #1
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    inequality word problem

    In creating a business plan for a cycle shop that seels both tricycles and bicycles, a business analyst graphed the inventory constraints set by the shop owner, and then shaded the region shown below where all of the constraints were met. Which of the following statements best defines the shaded region?

    The correct state is: The number of tricycles and bicycles together is less than 100, and the number of tricycles exceeds 30.
    Why is it less than 100 and exceeds 30? To me, it looks like it is 100??

    EDIT:
    The other (incorrect) choices that were included were:
    1) The number of tricycles exceeds 30, and the number of bicycles exceeds 30.
    2) The number of tricycles exceeds 30, and the number of bicycles is less than the number of tricycles.
    3) The number of tricycles is less than 100, and the number of bicycles is less than 100.
    4) The number of tricycles and bicycles together exceeds 100, and the number of bicycles is less than 100.
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  2. #2
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    When the number of tricycle is exactly 30, the number of bicycles is less than 70 (according to graph). So the production is less than 100. And when tricycle is greater than 30, total production is always < 100.
    Only when the bicycle production is zero, tricycle production is 100. Bur that case is not applicable.
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  3. #3
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    Quote Originally Posted by sa-ri-ga-ma View Post
    When the number of tricycle is exactly 30, the number of bicycles is less than 70 (according to graph).
    That means the intersection point right? Also, do we read this graph as any point in the shaded region is less than 100 (originally I read it as taking a point "x" and a point "y" from the respective axises and adding their values..) I've been trying to disprove each case that I posted above but I always get tripped up with reading the graph again..can everything be disproved by the fact that we know that intersection point?
    Last edited by sarahh; March 31st 2010 at 04:54 AM.
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