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A baker needs between 40 pounds and 50 pounds of a flour-sugar mixture that contains ten times as much flour as sugar. What are the possible weights of flour the baker can use?

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The question as it is does not restrict the answer to integral weights in pounds, so any between 40 and 50 pounds is a possible weight, W.
In order to satisfy the given proportion constraints, W/11=sugar, 10W/11=flour will ensure that the proportion be correct.
If the question specifies that the ingredient weights be integral (i.e. whole numbers), then W will have to be a multiple of 11, which makes 44 the only possible weight of mixture between 40 and 50, and the weight of flour is 10W/11=40 pounds.

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