Sarah plans to bake cookies for a charity event. She needs 2/3 cup of sugar for each batch of cookies. If sugar costs $1.50 per cup, how much will she spend on sugar if she bakes 12 batches of cookies? Additionally, if she finds a discount store where sugar costs $1.20 per cup, how much money will she save by buying sugar from the discount store instead? Let's think step by step and output the final answer within \boxed{}.
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