涛涛GWD 1-19

weifanmm

19。A total of $60,000 was invested for one year. But of this amount earned simple annual interest at the rate of X percent per year,and the rest earned simple annual interest at the rate of Y percent per year. If the total interest earned by the $60,000 for that year was $4080,what is the value of X?

(1) X=(3/4)Y

(2) the ration of the amount that earned interest at the rate of X percent per year to the amount that earned interest at the rate of Y percent per year was 3 to 2.

ANS:C

A+B=60000, X%A+X%B=4080

(2)A/B=3/2, A=36000,B=24000, (1)X%36000+(4/3)X%24000=4080

上面兰色的是有人给出的解释，我不懂为什么X%36000+(4/3)X%24000=4080不用乘上A，B各自存的时间？利息不是都要乘存的时间吗？

NN们解释一下，我的MATH有够烂的

federico0555

都是年利率，时间为1年。

 

lilyblue_zl

因为时间都说明是1年，同时x和y也都是一年期的利率，所以不用算月或者天。

bobiouous

 简单,不过我做的时候也错了,没看清楚.

给你列个四元一次方程组,你就知道怎么回事了:

这里X,Y我就不加%了

A+B=3/2

AX/BY=3/2

AX+BY=4080

X=3/4 *Y

具体算你就不要算了,小学老师以前教过我们,四个未知数要用四的等式关系才能解出,少一个关系式都不行,除非有可约的,这题没有.

所以一个不能少，才选C.

oldereaper

应该A+B=60000吧？

chouliulu

A+B=60000,

AX/BY=3/2

AX+BY=4080

X=3/4*Y

here,A=60000-B, X=3/4*Y

AX+BY=4080

=(60000-B)*3/4*Y+BY=4080

AX/BY=3/2

=[(60000-B)*3/4*Y]/BY=3/2

由上可知，二元二次方程，是可以解出来的，为什么C是错的?