作业帮一条外国数学题,解方程
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一条外国数学题,解方程
xy=2(x-5)(y-50)
xy(1+20%)=(x+10)(y-30)
答案是x=20
可以写出主要的运算过程,或其他计算方法
翻译可能有些不地道的地方和作了小修改.
有一群学生（x个）去租船开派对,费用每人平分.如果有5个学生请假不去了（x-5）,那么总费用便宜一半,而却剩下的学生每人可以少给50元.如果多10个学生去（x+10）,那么总费用就比原来贵20%,但是没人可以少个30元.问原来有多少个学生?
教科书原题：
A party of students rented a motor boat,B ,and shared to cost equally.if the number of students had been 5 less ,they could have used a smaller boat costing only half as much as B and the expense to each would have been 50 cents less.If there had been 10 more students in the party,they would have required a larger boat costing 20% more than B,but the expense to each would have been 30 cents less.How many students were in the party?
,但是解到一半的时候,同时出现了三次方,两次方和以次方的式子：-840x^3+800x+7500x^2+9700=0 请问你是怎么解的?
xy=2(x-5)(y-50)
xy(1+20%)=(x+10)(y-30)
答案是x=20
可以写出主要的运算过程,或其他计算方法
翻译可能有些不地道的地方和作了小修改.
有一群学生（x个）去租船开派对,费用每人平分.如果有5个学生请假不去了（x-5）,那么总费用便宜一半,而却剩下的学生每人可以少给50元.如果多10个学生去（x+10）,那么总费用就比原来贵20%,但是没人可以少个30元.问原来有多少个学生?
教科书原题：
A party of students rented a motor boat,B ,and shared to cost equally.if the number of students had been 5 less ,they could have used a smaller boat costing only half as much as B and the expense to each would have been 50 cents less.If there had been 10 more students in the party,they would have required a larger boat costing 20% more than B,but the expense to each would have been 30 cents less.How many students were in the party?
,但是解到一半的时候,同时出现了三次方,两次方和以次方的式子：-840x^3+800x+7500x^2+9700=0 请问你是怎么解的?
用代入消元法呀!直接展开二式,讲XY消去,记得到了X ,Y关系,用X表示Y,带入原方程中,即可解出X
不可能出现三次方的呀!
xy+500=100x+10y①;
xy+1500=50y-150x②
相减并化简得：4y-25x=100;25x=4y-100③;代入①得：
0.08y^2-15y+900=0;易得△=81 由题意知：y>50
∴y=150,代入③即得：x=20
简单方法暂时没有想出来!
不可能出现三次方的呀!
xy+500=100x+10y①;
xy+1500=50y-150x②
相减并化简得：4y-25x=100;25x=4y-100③;代入①得：
0.08y^2-15y+900=0;易得△=81 由题意知：y>50
∴y=150,代入③即得：x=20
简单方法暂时没有想出来!