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Solution to: All Apples

The big pile of apples contains the same amount of large apples of a quarter of a euro each (from Mrs. Jones), as smaller apples of one sixth euro each (from Mrs. Smith). The average price is therefore (1⁄4 + 1⁄6) / 2 = 5⁄24 euro. However, apples are sold for 1⁄5 euro each (5 apples for 1 euro). This means that per sold apple there is a shortage of 5⁄24 - 1⁄5 = 1⁄120 euro. The total shortage is 3.50 euro, so the women together started out with 420 apples. These are worth 1⁄5 × 420 = 84 euro, or with equal division 42 euro for each. If Mrs. Jones had sold her 210 apples herself, she would have received 52.50 euro.

Conclusion: Mrs. Jones loses 10.50 euro in this deal.


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