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Math Help - Inverse relation word problem

  1. #1
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    Inverse relation word problem

    If 12 bags of food will feed 6 dogs for 18 days, then how many days will 12 bags of food feed 9 dogs?

    The answer is 12 but I just can't see it
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mjoshua View Post
    If 12 bags of food will feed 6 dogs for 18 days, then how many days will 12 bags of food feed 9 dogs?

    The answer is 12 but I just can't see it
    Assume that each dog gets the same amount of food.

    Thus, each dog will eat 2 bags of food every 18 days (from the given information at the start of the problem).

    But that means the dog eats 2/18=1/9 bag per day.

    Now, we have to consider feeding the 9 dogs with 12 bags of food. Since each dog eats 1/9 bag per day, that means the 9 dogs eat 1 bag per day. Now, since there are 12 bags available, how many days will it take the 9 dogs to eat them?
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    Are there any alternate explanations for this problem? For some reason, I still don't see it
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  4. #4
    Senior Member Educated's Avatar
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    If 12 bags of food will feed 6 dogs for 18 days, then how many days will 12 bags of food feed 9 dogs?

    12 bags of food will feed 6 dogs for 18 days
    Therefore 2 bags of food will feed 1 dog for 18 days

    So, \frac{2}{18} bags of food will feed 1 dog for 1 day.

    In 1 day, 9 dogs will eat 9 \times \frac{2}{18} bags of food. This means that in 1 day, 9 dogs will eat exactly 1 bag of food.

    Therefore with 12 bags of food, it will feed the 9 dogs for 12 days.
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