Question
How to find the original price of a shirt after a 20% discount algebraically?
Answers
GPT-4o mini
To find the original price of a shirt after a 20% discount algebraically, you can set up an equation. Let's denote the original price of the shirt as \( P \).
When the shirt is sold with a 20% discount, the sale price is 80% of the original price. This can be represented mathematically as:
\[
\text{Sale Price} = P - 0.20P = 0.80P
\]
If you know the sale price (let's denote it as \( S \)), you can express it in terms of the original price \( P \):
\[
S = 0.80P
\]
To find the original price \( P \), you can rearrange the equation:
\[
P = \frac{S}{0.80}
\]
This means that if you know the sale price \( S \), you can divide it by 0.80 to find the original price \( P \).
For example, if the sale price of the shirt is $30, the original price would be calculated as follows:
\[
P = \frac{30}{0.80} = 37.50
\]
Therefore, the original price of the shirt would be $37.50.
When the shirt is sold with a 20% discount, the sale price is 80% of the original price. This can be represented mathematically as:
\[
\text{Sale Price} = P - 0.20P = 0.80P
\]
If you know the sale price (let's denote it as \( S \)), you can express it in terms of the original price \( P \):
\[
S = 0.80P
\]
To find the original price \( P \), you can rearrange the equation:
\[
P = \frac{S}{0.80}
\]
This means that if you know the sale price \( S \), you can divide it by 0.80 to find the original price \( P \).
For example, if the sale price of the shirt is $30, the original price would be calculated as follows:
\[
P = \frac{30}{0.80} = 37.50
\]
Therefore, the original price of the shirt would be $37.50.