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[数论] 应用题

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lrh2006 posted 2022-4-5 14:25 |Read mode
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战巡 posted 2022-4-5 21:11
回复 1# lrh2006


假设A每包$p$千克,A、B各卖出$x,y$包

那么有
\[\begin{cases}px+4y=1000\\30x+64y-8400-2000=4800\end{cases}\]
第二个化简有
\[15x+32y=7600\]
那么第一个乘以8减去第二个,得到
\[(8p-15)x=400\]
这里$x\ge y$,说明
\[15x+32x\ge 15x+32y=7600\]
\[x\ge \frac{7600}{47}\approx 161.7\]
而鉴于$8p-15\ne 0$,那么必须有$x$整除$400$,$x=200$或$400$。

当$x=200$时,$8p-15=2$,显然是不可能的,踢掉
当$x=400$时,$8p-15=1$,$p=2$,成立
因此就是400包了

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original poster lrh2006 posted 2022-4-6 15:54
回复 2# 战巡

谢谢战巡老师!
哎,我又差了一点,没有把条件用全

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