Question

during a sale all items are discounted by 50%.
you arrive at the store and there is a sign, \take an additional 20% off the latest discounted price.\
a. does that mean that all items are 70% off?
b. if the regular price of a sweater is $84, how much will you pay for it? $

Explanation:

Step1: Analyze part a

Let the original price be \(P\). After a \(50\%\) discount, the price is \(P(1 - 0.5)=0.5P\). Then, taking an additional \(20\%\) off the latest - discounted price. The new price is \(0.5P(1 - 0.2)=0.5P\times0.8 = 0.4P\). The total discount is \(1-0.4 = 0.6\) or \(60\%\) off, not \(70\%\) off.

Step2: Calculate part b

The regular price of the sweater \(P = 84\).
First, after a \(50\%\) discount, the price \(P_1=84\times(1 - 0.5)=84\times0.5 = 42\).
Then, after an additional \(20\%\) discount, the price \(P_2=42\times(1 - 0.2)\).
We know that \(42\times(1 - 0.2)=42\times0.8=\frac{42\times8}{10}=33.6\).

Answer:

a. No
b. \(33.6\)