A woman had three old coins - a silver dollar, a quarter, and a dime. Each coin was a little battered and had a piece missing. She found that exactly the same fraction had broken away from each coin.

What fraction of each was missing if the value of the remaining bits of coins was now exactly one dollar in total?

For this puzzle it can be assumed that ½ of a coin is worth ½ of its value.

Based on a puzzle by Henry Ernest Dudeney.

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Answer

7÷27 of each coin was missing.

The original value of the three coins was 100 + 25 + 10 = 135, and the new value was 100. So 35÷135 of the original value has been removed and 35÷135 = 7÷27.

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