Assume that a.b.c.d are integers.and four equations y=1.z=1.w+100=d have always solutions x.y.z.w of positive numbers respectively.then the minimum of a is 2433．(英汉词典:to assume假设,integer整数,equation方� 题目和参考答案——青夏教育精英家教网—

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20、Assume that a，b，c，d are integers，and four equations （a-2b）x=1，（b-3c）y=1，（c-4d）z=1，w+100=d have always solutions x，y，z，w of positive numbers respectively，then the minimum of a is

2433

．
（英汉词典：to assume假设；integer整数；equation方程；solutions （方程的）解；positive正的；respectively分别地；minimum最小值）!

分析：根据四个方程都有正的解可得a＞2b，b＞3c，c＞4d，d＞100，从而可得出d的最小值，进而可分别求得c、b、a的最小值．

解答：解：∵四个方程都有正的解，
∴a＞2b，b＞3c，c＞4d，d＞100，
∴可得d_min=101，
又∵c＞4d=404，得出c_min=405，
b＞3c=1215，得出b_min=1216，
a＞2b=2432，得出a_min=2433．
故答案为：2433．

点评：本题是结合英语考查的关于整数问题综合运用的试题，比较新颖，解答本题的关键是理解题意，根据d＞100得出d的最小值，进而依次求出c、b和a的最小值．

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