想不通的问题

DreamHospital

A chemist has x liters of sugar solution that is x% sugar. How many liters of sugar must be added to this solution to yield a sugar solution that is 3x% sugar?

每次我做到的答案都是2x^2/100。但正确答案是2x^2/(100-3x)

flash

原帖由 DreamHospital 于 27-10-2009 03:42 PM 发表
A chemist has x liters of sugar solution that is x% sugar. How many liters of sugar must be added to this solution to yield a sugar solution that is 3x% sugar?

每次我做到的答案都是2x^2/100。但正确答 ...

是思考角度的问题。。。。

你的想法可能是把固体的糖加入液体中（容量不会增加），而题目的要求是把液体的糖加入液体中（容量过后会增加）。


假设 a 是原本糖的份量，k 是将加入的份量。

a/x * 100 = x
a = x^2/100

(a+k)/(x+k) * 100 = 3x
k(100 - 3x) = 3x^2 - 100a
k = (3x^2 -100a) / (100 - 3x) = 2x^2/(100 - 3x)

[ 本帖最后由 flash 于 27-10-2009 07:52 PM 编辑 ]

DreamHospital

原来是这样，谢谢您