四年级奥数题及答案:卖油(高等难度)
卖油:(高等难度)甲乙两个油桶各装了15千克油.售货员卖了14千克.后来,售货员从剩下较多油的甲桶倒一部分给乙桶使乙桶油增加一倍;然后从乙桶倒一部分给甲桶,使甲桶油也增加一倍,这时甲桶油恰好是乙桶油的3倍.问:售货员从两个桶里各卖了多少千克油?
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卖油答案:
解题关键是求出甲、乙两个油桶最后各有油多少千克.已知"甲、乙两个油桶各装油15千克.售货员卖了14千克".可以求出甲、乙两个油桶共剩油15×2-14=16(千克).又已知"甲、乙两个油桶所剩油"及"这时甲桶油恰是乙桶油的3倍".就可以求出甲、乙两个油桶最后有油多少千克.
求出甲、乙两个油桶最后各有油的千克数后,再用倒推法并画图求甲桶往乙桶倒油前甲、乙两桶各有油多少千克,从而求出从两个油桶各卖出多少千克.
解:①甲乙两桶油共剩多少千克?
15×2-14=16(千克)
②乙桶油剩多少千克?16÷(3+1)=4(千克)
③甲桶油剩多少千克?4×3=12(千克)
用倒推法画图如下:
http://www.aoshu.com/e/20110921/data:image/png;base64,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
④从甲桶卖出油多少千克? 15-11=4(千克)
⑤从乙桶卖出油多少千克? 15-5=10(千克)
答:从甲桶卖出油4千克,从乙桶卖出油10千克.
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