A greengrocer sold a case of apples in the following way.The first customer bought half the case, plus another two apples.The second customer bought half of those left, plus another two apples.The third customer bought half those left, plus another two apples.The fourth customer bought the remaining apple.How many apples were in the case originally?
Question
A greengrocer sold a case of apples in the following way.The first customer bought half the case, plus another two apples.The second customer bought half of those left, plus another two apples.The third customer bought half those left, plus another two apples.The fourth customer bought the remaining apple.How many apples were in the case originally?
Solution
Let's solve this problem step by step:
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Let's denote the original number of apples as X.
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According to the problem, the first customer bought half the case, plus another two apples. So, the remaining apples after the first customer are X/2 - 2.
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The second customer bought half of those left, plus another two apples. So, the remaining apples after the second customer are (X/2 - 2)/2 - 2 = X/4 - 3.
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The third customer bought half those left, plus another two apples. So, the remaining apples after the third customer are (X/4 - 3)/2 - 2 = X/8 - 4.5.
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The fourth customer bought the remaining apple. So, X/8 - 4.5 = 1.
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Solving the equation X/8 - 4.5 = 1 for X gives X = 8 * (1 + 4.5) = 44.
So, the greengrocer originally had 44 apples in the case.
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