甲、乙两容器内都盛有酒精,甲有v1千克,乙有v2千克．甲中纯酒精与水（重量）之比为m1：n1,乙中纯酒精与水之比为m2：n2,求甲中纯酒精是乙中纯酒精的多少倍

Question

甲、乙两容器内都盛有酒精,甲有v1千克,乙有v2千克．甲中纯酒精与水（重量）之比为m1：n1,乙中纯酒精与水之比为m2：n2,求甲中纯酒精是乙中纯酒精的多少倍

Answer 1

甲中纯酒精重量是：v1×m1/(m1+n1)
乙中纯酒精重量是：v2×m2/(m2+n2)
甲中纯酒精是乙中纯酒精的v1×m1×(m2+n2)/[v2×m2×(m1+n1)]
甲中水的重量是：v1×n1/(m1+n1)
乙中水的重量是：v2×n2/(m2+n2)
总共纯酒精重量为：v1×m1/(m1+n1)+v2×m2/(m2+n2)
=(v1m1m2+v1m1n2+v2m1m2+v2m2n1)/(m1+n1)(m2+n2)
总共水的重量为：v1×n1/(m1+n1)+v2×n2/(m2+n2)
=(v1n1m2+v1n1n2+v2m1n2+v2n1n2)/(m1+n1)(m2+n2)
所得液体中纯酒精与水之比是:
(v1m1m2+v1m1n2+v2m1m2+v2m2n1)/(v1n1m2+v1n1n2+v2m1n2+v2n1n2)