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Math Help - Using basic algebra + math to solve word problem

  1. #1
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    Using basic algebra + math to solve word problem

    First off, here's the word problem:
    Alex and his parents went to the grocery store to buy some candy. They came home with 96 individually wrapped candies, and started eating them. Alex, being the sweet tooth, can eat 48 candies an hour. His dad can eat 16 candies an hour, while his mom isn't too fond of sweets, eating only 2 candies an hour. How long would it take Alex and his parents to eat all 96 candies? Round your answer to the nearest minute.

    First off, here's my work:
    48x + 16x + 2x = 96

    Then I reduced it:
    24x + 8 x + x = 48

    Then I added up the variables:
    33x = 48

    Then I simply divided 48 by 33, and got 1.45454545.... and so on. I subtracted 1, as the 1 would represent 1 hour, or 60 minutes. I then took the remaining 0.454545... and multiplied by 60 to get 27.272727....

    After that, I simply rounded up to 28, and added the hour on, giving me a total of 1:28 or 88 minutes.

    Now, either I'm doing something wrong or the answer key is wrong, because when I checked it, the key said 94.

    Any help would be much appreciated, and thanks in advance.
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  2. #2
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    Quote Originally Posted by DannyMerrell View Post
    First off, here's the word problem:
    Alex and his parents went to the grocery store to buy some candy. They came home with 96 individually wrapped candies, and started eating them. Alex, being the sweet tooth, can eat 48 candies an hour. His dad can eat 16 candies an hour, while his mom isn't too fond of sweets, eating only 2 candies an hour. How long would it take Alex and his parents to eat all 96 candies? Round your answer to the nearest minute.

    First off, here's my work:
    48x + 16x + 2x = 96

    Then I reduced it:
    24x + 8 x + x = 48

    Then I added up the variables:
    33x = 48

    Then I simply divided 48 by 33, and got 1.45454545.... and so on. I subtracted 1, as the 1 would represent 1 hour, or 60 minutes. I then took the remaining 0.454545... and multiplied by 60 to get 27.272727....

    After that, I simply rounded up to 28, and added the hour on, giving me a total of 1:28 or 88 minutes.

    Now, either I'm doing something wrong or the answer key is wrong, because when I checked it, the key said 94.

    Any help would be much appreciated, and thanks in advance.
    Mathematically, I agree with your answer.

    However, since the eating continues into the second hour, Alex's mother will eat 3 of the candies. And since it takes her half an hour to eat each one, I'd argue that technically it will take 90 minutes for all the candies to be eaten.
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  3. #3
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    I wouldn't use algebra in this case, I'd use the ratio hours : proportion of the sweets eaten for each person

    Alex \displaystyle 1 : \frac{1}{2}

    Dad \displaystyle 1 : \frac{1}{6}

    Mum \displaystyle 1 : \frac{1}{48}.


    So every hour, together \displaystyle \frac{1}{2} + \frac{1}{6} + \frac{1}{48} = \frac{24}{48} + \frac{8}{48} + \frac{1}{48} = \frac{33}{48} of the sweets are eaten.

    Together \displaystyle 1 : \frac{33}{48}

    \displaystyle 48 : 33

    \displaystyle \frac{48}{33} : 1.


    So together, it will take \displaystyle \frac{48}{33} hours, or approximately \displaystyle 1\,\textrm{hr}\, 27\,\textrm{min}.
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    Mathematically, I agree with your answer.

    However, since the eating continues into the second hour, Alex's mother will eat 3 of the candies. And since it takes her half an hour to eat each one, I'd argue that technically it will take 90 minutes for all the candies to be eaten.
    Does it take her half an hour to eat each one? There's nothing saying that her consumption is at an even pace, so I don't think you can assume that.

    For what it's worth I used function notation to solve. :P
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  5. #5
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    Quote Originally Posted by Prove It View Post
    I wouldn't use algebra in this case, I'd use the ratio hours : proportion of the sweets eaten for each person

    Alex \displaystyle 1 : \frac{1}{2}

    Dad \displaystyle 1 : \frac{1}{6}

    Mum \displaystyle 1 : \frac{1}{48}.


    So every hour, together \displaystyle \frac{1}{2} + \frac{1}{6} + \frac{1}{48} = \frac{24}{48} + \frac{8}{48} + \frac{1}{48} = \frac{33}{48} of the sweets are eaten.

    Together \displaystyle 1 : \frac{33}{48}

    \displaystyle 48 : 33

    \displaystyle \frac{48}{33} : 1.


    So together, it will take \displaystyle \frac{48}{33} hours, or approximately \displaystyle 1\,\textrm{hr}\, 27\,\textrm{min}.
    This question is an example of where rounding UP is required because the candies will not quite be eaten at 1 hour 27 minutes ....

    (Hmppph, I quite liked my consumption assumption).
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    (Hmppph, I quite liked my consumption assumption).
    I like to think they all sit around as a family and wait till the 59th minute of each hour and eat them all at once. haha, so I guess it could also take 2 hours with the right assumptions.
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