AMC8 2012

AMC8 2012 · Q8

AMC8 2012 · Q8. It mainly tests Percent, Arithmetic misc.

A shop advertises that everything is “half price in today’s sale.” In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage discount off the original price?

一家商店宣传“今日特卖一切商品半价”。此外，一张优惠券在特卖价基础上再打8折。使用优惠券，今天的价格相对于原价是多少折扣百分比？

(A) 10 10

(B) 33 33

(D) 60 60

(E) 70 70

Answer

Correct choice: (D)

正确答案：（D）

Solution

Let the original price of an item be $x$. First, everything is half-off, so the price is now $\frac{x}{2} = 0.5x$. Next, the extra coupon applies 20% off on the sale price, so the price after this discount will be $100\% - 20\% = 80\%$ of what it was before. (Notice how this is not applied to the original price; if it were, the solution would be applying 50% + 20 % = 70% off the original price.) $80\% \cdot 0.5 x = \frac{4}{5} \cdot 0.5 x = 0.4x$ The price of the item after all discounts have been applied is $0.4x = 40\% \cdot x$. However, we need to find the percentage off the original price, not the current percentage of the original price. We then subtract $40\% x$ from $100\% x$ (the original price of the item), to find the answer, $\boxed{\textbf{(D)}\ 60}$.

假设物品原价为$x$。首先，一切商品半价，所以价格变为$\frac{x}{2} = 0.5x$。接下来，优惠券在特卖价基础上打8折，即$100\% - 20\% = 80\%$的原价。（注意，这不是直接在原价上打折；如果是那样，会是50% + 20% = 70%折扣。） $80\% \cdot 0.5 x = \frac{4}{5} \cdot 0.5 x = 0.4x$ 所有折扣后价格是$0.4x = 40\% \cdot x$。但是我们需要找出相对于原价的折扣百分比。从$100\% x$（原价）中减去$40\% x$，得到答案$\boxed{\textbf{(D)}\ 60}$。

Topics