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More math problems, please help me!!? |
A private art collector who buys a valuable canvas is later forced to sell it to an art gallery at a 10% loss during financial depression. Some years later, she rebuys it at auction and sells it to a museum for $37,000 more than the auction price. In the gallery made 25% profit and the collector made a 39.5% net profit on her original investment, for what price did she originally buy the picture? Two railroad workers are together in a 0.6-mile mountain tunnel. one walks east and the other west in order to be out of the tunnel before the Bad Creek Express comes through 30mph. Each man reaches his respective end of the tunnel in 3 min. If the man walking east reaches the east entrance just before the train enters, and the train passes the other man 0.12 miles beyond the west end of the tunnel, at what rate did each man walk? I will do the first. Let X be the amount the collector paid for the painting. 1) She sold it during the depressions, and the price was .9X (she lost 10%). 2) She rebuys it at auction, for Y dollars. At this point, the gallery made a 25% profit, or Y = 1.25(.9X). 3) She sells it to a museum for Y + 37000. At this point, the collector made a 39.5% net profit on her original investment, of X dollars, i.e., Y + 37000 = 1.395X. 4) Putting (2) and (3) together, we have 1.25(.9X) + 37000 = 1.395X. 1.125X + 37000 = 1.395X; gather like terms 37000 = 1.395X - 1.125X, or 37000 = 0.27X, divide both sides by 0.27 x = 37000/0.27 = 137037 dollars. Go through the story again, and check the answer. |
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