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To answer this requires only that you find the volume of a quarter coin, and divide the volume of the container by the volume of a quarter. This will give you a very close approximation, since obviously the coins cannot fit into every tiny space within the jug -- there will be some unfilled volume.

Volume of a US quarter = approx. 808.93 mm3 or 0.80893 cm3

Volume of a US gallon = 3785.41178 cm3

Dividing the jug volume by the quarter's volume we get

3785.41178 / 0.80893 = slightly less than 4680 quarters($1170 USD).

One test using a 5-gallon jug provided a ballpark figure of $5200, so an actual experimental value would be closer to 4160 quarters. ($1040 USD)

(see related question)

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Estimate By Weight

A quarter is mostly copper, and by weight a gallon of quarter metal (copper and 8.33% zinc) would weigh about 33760 grams, as much as 5950 quarters. This indicates that the quarter takes up some empty space. The weight of 0.808 cm3 of solid metal would be 7.20 grams not the official weight of 5.67 grams.

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