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In the movie Once Upon a Time in America, set in the Prohibition era, a clever ploy is used by bootleggers transporting liquor by boat. Attached to each case of liquor is a balloon of negligible weight and a cloth bag filled with salt as shown in the figure below. When police approach, the liquor is dumped overboard. Initially the cases sink, but after a time the salt dissolves and the balloons float to the surface. Suppose that a liquor case weighs 175 N and displaces 137 N of water and that, when the balloon floats, it is half submerged. Find the volume of the balloon and the required weight of salt.

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