Sure, let's break this problem down step-by-step:
1. Understanding a 40% Discount:
- When an item is discounted by 40%, it means the price is reduced by 40% of its original price.
2. Representing the Original Price:
- Let the original price of the item be denoted by [tex]\( p \)[/tex].
3. Calculating the Amount of the Discount:
- A 40% discount on the price [tex]\( p \)[/tex] is calculated as [tex]\( 0.4 \times p \)[/tex].
4. Finding the Discounted Price:
- To find out how much the item costs after the discount, you subtract the discount from the original price:
[tex]\[
\text{Discounted Price} = p - 0.4 \times p
\][/tex]
- Simplifying this expression:
[tex]\[
\text{Discounted Price} = p - 0.4p = 0.6p
\][/tex]
- Therefore, the discounted price of the item can be represented by [tex]\( 0.6p \)[/tex].
5. Alternative Representation:
- Realizing that a 40% discount means you are paying 60% of the original price ([tex]\( 100\% - 40\% = 60\% \)[/tex]), you can directly express it as:
[tex]\[
\text{Discounted Price} = 60\% \times p = 0.6 \times p
\][/tex]
6. Summarize the Two Expressions:
- The first expression representing a 40% discount on the price [tex]\( p \)[/tex] of an item:
[tex]\[
p - 0.4p
\][/tex]
- The second expression representing a 40% discount on the price [tex]\( p \)[/tex] of an item:
[tex]\[
0.6p
\][/tex]
Hence, we have written two expressions that can be used to represent a 40% discount on the price [tex]\( p \)[/tex] of an item. Both expressions fundamentally convey the same mathematical idea but presented in slightly different forms.
