这道Prep数学题很疑惑，麻烦大家帮我看看

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关于条件2，

设价格从低到高为x,y,z ；则假设不等式 (z*1/5 +(15+y)*1/10) / (15+y+z)>1/15 ;

化简后得到不等式 4z+y+15 >0; 恒成立，因此，假设的不等式成立，因此条件2充分；

不知道我错在哪？

先谢过！

根據條件一
假設x=50, z=20可得1/5*50+1/10*y+1/10*20=12+0.1Y,等式右邊為15/100*(50+y+20)=10.5+0.15Y,

若三個折扣相加>15%*三個物品原價,則y<30

若三個折扣相加<15%*三個物品原價,則y>30,

所以可知y>或是<30將會影響,因此根據條件一,不足以判斷三個折扣相加>或是<15%*三個物品原價.

因此需要結合條件二

x=50,y=20,z=15,才能斷定1/5*50+1/10*20+15*1/10=13.5;15/100*(50+20+15)=12.75

可知三個折扣相加>15%*三個物品原價

答案為C,結合兩個條件可知

Assume the price of the least expensive is x.

Then the total discount is: 50*20%+20*10%+x*10% = 12 + 0.1x, the total cost before discount is: 50+20+x = 70 +x.

The discount rate is:

(12+0.1x)/(70+x).

In order for the discount rate to be greater than 15%, the following should be true:

(12+0.1x)/(70+x) > 15%

12 + 0.1x > 70 * 0.15 + 0.15x

1.5 > 0.05x

x< 30

Since the second expensive item is $20, the third one must be less than $20, which is less than $30, therefore, the total discount is greate than 15%.

So, the answer should be A.

楼上这位同学的解法exactly correct,但是好像忽视了解释条件二,我补充一下.

条件二可以这样表达0.2x+0.1y+1.5)/x+y+15>0.15,化简以后4x+2y+30>3x+3y+45,最后等于x-y>15,题上没有满足这个条件,所以只能选A