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Math Help - very hard inversely proportional

  1. #1
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    very hard inversely proportional

    Hi this is my question:
    The grant avalible to a section of society was inversely proportional to the number of people needing the grant. When 30 people needed a grant, the received 60 each.

    i worked out that K=1800
    But:
    a) what would the grant have been if 120 people had needed one?
    i get stuck on this bit, would i do this to get the answer?
    120/30=4 1800 x 4= 7200?????
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by andyboy179 View Post
    Hi this is my question:
    The grant avalible to a section of society was inversely proportional to the number of people needing the grant. When 30 people needed a grant, the received 60 each.

    i worked out that K=1800
    But:
    a) what would the grant have been if 120 people had needed one?
    i get stuck on this bit, would i do this to get the answer?
    120/30=4 1800 x 4= 7200?????
    The relationship of inversely proportional variables is: y = \frac{k}{x}

    In this case y is the amount of grant and x the number of people. You found k (and it's correct) so simply sub your value of k in when x = 120

    y = \frac{k}{120} = \frac{1800}{120} = \frac{180}{12} = \frac{60}{4} = 15


    -----------------------------------------

    Another way to think about it is that every time the number of people double the grant will be half of the previous amount.

    As 120/30 = 4 then it follows it will be a quarter of the original amount: 60/4 = 15
    Last edited by e^(i*pi); January 26th 2010 at 07:16 AM. Reason: because I suck at cancelling fractions - correct answer now
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  3. #3
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    thanks.
    can you help me on this question aswell?
    b) if the grant had been 50 each, how many people would have received it?
    would i do:
    1800/50= 36 people?
    Last edited by andyboy179; January 26th 2010 at 08:07 AM. Reason: being impolite
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by andyboy179 View Post
    thanks.
    can you help me on this question aswell?
    b) if the grant had been 50 each, how many people would have received it?
    would i do:
    1800/50= 36 people?
    You can do either \frac{36}{30} \times 30 or you can use the equation:

    x = \frac{1800}{50}

    Both of these give an answer of 36 so you're correct
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