To determine which expressions correctly represent the sale price of an item that is on sale for 20% off the regular price [tex]\( p \)[/tex], let's analyze each expression step-by-step:
1. The regular price of the item is [tex]\( p \)[/tex] dollars.
2. A discount of 20% off means we are taking 20% of [tex]\( p \)[/tex]. This can be written as:
[tex]\[ 0.2 \times p \][/tex]
3. To find the sale price, we subtract this discount from the original price:
[tex]\[ p - 0.2 \times p \][/tex]
4. Simplify the expression:
[tex]\[ p - 0.2p = 0.8p \][/tex]
Now, let's evaluate each of the given expressions to see which ones represent this sale price:
- Expression A: [tex]\( 0.2 p \)[/tex]
- This represents the discount amount, not the sale price.
- Expression B: [tex]\( 0.8 p \)[/tex]
- This represents the sale price. Correct!
- Expression C: [tex]\( 1 - 0.2 p \)[/tex]
- This expression is incorrect. It does not logically represent a price calculation.
- Expression D: [tex]\( p - 0.2 p \)[/tex]
- This simplifies to [tex]\( 0.8 p \)[/tex], which represents the sale price. Correct!
- Expression E: [tex]\( p - 0.8 p \)[/tex]
- This simplifies to [tex]\( 0.2 p \)[/tex], which is the remaining 20% and thus not correct for the sale price.
The correct expressions that each represent the sale price of the item are:
[tex]\[ 0.8 p \][/tex] and [tex]\[ p - 0.2 p \][/tex]
These correspond to Expression B and Expression D, respectively.
Therefore, the correct answer is:
C. Expression B and Expression D
