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Math Help - ord problem...how do I write this out in Algebra (ratio and proportion) form?

  1. #1
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    ord problem...how do I write this out in Algebra (ratio and proportion) form?

    I know the answer is 9, however I do not know how to show the formula I used to arrive at the answer!:

    A cake recipe serves 4 people, and calls for 1.5 cups of flour and 2.5 cups of sugar. In the cupboard there is 3.5 cups of flour, and 10.25 cups of sugar. Using the recipe to make the largest cake possible with the all ingredients, how many people will it serve?

    I know the problem lies with the flour I eed to know lso te ratio of extra sugar to the extra .5 cup of flour! I appreciate your help in showing me the steps, and how to write this out so that it makes sense, in algebra terms!!!
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  2. #2
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    Quote Originally Posted by Isdene View Post
    I know the answer is 9, however I do not know how to show the formula I used to arrive at the answer!:

    A cake recipe serves 4 people, and calls for 1.5 cups of flour and 2.5 cups of sugar. In the cupboard there is 3.5 cups of flour, and 10.25 cups of sugar. Using the recipe to make the largest cake possible with the all ingredients, how many people will it serve?

    I know the problem lies with the flour I eed to know lso te ratio of extra sugar to the extra .5 cup of flour! I appreciate your help in showing me the steps, and how to write this out so that it makes sense, in algebra terms!!!
    A quick way without worrying about exactly how much sugar you need is to see that 3.5/1.5 = 7/3. multiply 4 by (7/3) to get 28/3, or 9.333~. Thus, you can feed 9 and one third people, or really just 9.
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  3. #3
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    The long method:

    Try to compute for how many cups(mixture of flour/sugar) per person, so add 1.5 cups(flour) and 2.5 cups(sugar) = 4

    4 cups(mixture of flour/sugar) : 4 people
    therefore 1 cup : 1 person

    in the problem it says that there are 3.5 cups of flour and 10.25 cups of sugar, as we can observe that there is an excess of cups of sugar. So to solve for how many cups of sugar...

    1.5(flour) : 3.5(flour) = 2.5(sugar) : x
    where x = cups of sugar needed to make the cake

    1.5x = (3.5)*(2.5)

    1.5x = 8.75

    x = 5.8333...

    so in the new cake there are 3.5 cups of flour and 5.8333... cups of sugar, then add them so we will have 9.333... cups(mixture of flour/sugar)
    By looking at the ratio 1 cup : 1 person, we can now compute for the answer

    ...9.333...cups(mixture of flour/sugar) : 9.333...persons

    therefore the answer is 9.
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