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Math Help - inequalities?

  1. #1
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    inequalities?

    Hi guys,

    it's been a really long while since i've done anything but basic math. i don't know how to solve this problem and my textbook doesn't give an example at all. I'm hoping someone can help.

    The problem:

    Mary and her band receives $550 plus 15% of receipts over $550 for playing a gig. If a club charges a $6 cover charge, how many people must attend in order for Mary and her band to receive $1200?
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  2. #2
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    Quote Originally Posted by kohane View Post
    Hi guys,

    it's been a really long while since i've done anything but basic math. i don't know how to solve this problem and my textbook doesn't give an example at all. I'm hoping someone can help.

    The problem:

    Mary and her band receives $550 plus 15% of receipts over $550 for playing a gig. If a club charges a $6 cover charge, how many people must attend in order for Mary and her band to receive $1200?
    As far as I understand the problem there must be an income(?) of:


    \bullet~~\$ 550

    \bullet~~\dfrac{\$ 1200 - \$550}{0.15} = \dfrac{\$ 13,000}{3} \approx \$ 4333.3

    which yield a total of \$ 4883.3

    To get this amount there must be 814 visitors, listeners,
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  3. #3
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    hi thanks for your help. But at least how many people must attend? how would we set up the equation?
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  4. #4
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    Quote Originally Posted by kohane View Post
    hi thanks for your help. But at least how many people must attend? how would we set up the equation?
    Let x \in \mathbb{N} denote the number of listeners. Collect all results and solve for x:

    6 \frac{\$}{person} x \geq \$ 550 + \dfrac{\$ 1200 - \$550}{0.15}~\implies~x \geq 814 \ persons
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  5. #5
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    kohane, here's one approach for progressing from a verbal rendering of the situation, to the algebraic inequality earboth gave you...



    The question can be though of as, How many tonedeaf (I've heard Mary's band) people must attend, so that
    • The amount that the band will receive, based on the agreement,
    • will be at least
    • $1,200?
    One at a time, and letting x denote the number of listeners, sticking with earboth's notation...
    • The amount the band will receive, at 6 bucks a head, is 550 + 0.15(6x - 550)
    • "will be at least" can be rendered as "greater than or equal to", aka  \geq
    • 1,200 is, well, 1,200
    Stringing the three components together, the question can thus be expressed as

    550 + 0.15(6x - 550)  \geq 1,200

    ...and then solving for x will get you to earboth's solution. I hope that helped a bit. Best of luck.
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