A van is delivering 180 bottles of drinks to a neighborhood, and each bottle contains either cider or beer or a mixture of two. Out of the 180 bottles, 40 contain only cider, 80 contain only beer, and the rest are a mixture of the two drinks. If the delivery man gives half the number of each bottle of drink to the first house, how many bottles does the first house get?
Thoughts? Step-by-step reasoning:
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The total number of bottles containing cider or beer is 40 + 80 = 120. If the number of bottles in the van was 180, then 180 - 120 = 60 contains a mixture of the two drinks. At the first house, the delivery man dropped 1 / 2 * 40 = 20 bottles. There were also 1 / 2 * 80 = 40 bottles of beer that the delivery man gave to the first house. Together, the first house received 40 + 20 = 60 bottles of cider and beer. The total number of bottles that had a mixture of the two drinks that were dropped at the first house is 1 / 2 * 60 = 30. The first house got 60 + 30 = 90 bottles of all types of drinks.
Thus, the answer is 90.
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