请帮忙看道数学题，多谢各位了

lijia1301981

麻烦大侠帮忙看道数学题，答案在下面，不知道怎么解，谢谢各位帮助！

Q28:

This year Henry will save a certain amount of his income, and he will spend the rest.  Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend.  In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

 

E.     
                                

1/(2r+3)

vivi783

假设H兄去年存了s，那么“for each dollar that he saves this year,he will have 1 + r dollars available to spend”，他今年有s(r+1)可以花，再由于H今天花的钱是去年的一半，所以去年花了2s(r+1)，那么H去年一共挣了s+2s(r+1),比值就是s/s+2s(r+1),将s约掉后，为答案。

我解释能力有限，希望你能明白

lijia1301981

好复杂，绕了半天终于想明白了，高人啊，多谢了！

candy_yue

假设fraction是x

今年存款=x*今年收入

今年开销=(1-x)*今年收入

明年开销=今年存款*(1+r)=x*今年收入*(1+r)

要求：明年开销=0.5*今年开销

x*今年收入*(1+r)=0.5*(1-x)*今年收入

两边约去，x=1/(3+2r)