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A bag contains nickels, dimes, and quarters. Nickels weigh 5.0 grams apiece, dimes weigh 2.3 grams...

A bag contains nickels, dimes, and quarters. Nickels weigh 5.0 grams apiece, dimes weigh 2.3 grams apiece and quarters weigh 5.7 grams apiece. The bag contains a total of 276 coins with a total weight of 1088.5 grams and a total value of $31.55. How many coins of each type are there?

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