- Identify the discount as 20% of the original price \(P\), expressed as \(0.20P = 13\).
- Solve for the original price by dividing the savings by the discount rate: \(P = \frac{13}{0.20}\).
- Calculate the result: \(P = 65\).
- The original price is \(\boxed{\$65}\).
Explanation
- Analysis of the Problem
We are given that a store offers a \(20\%\) discount on all items. Mai purchased an item and saved \(\$13\). We need to determine the original price of the item before the discount was applied. Let \(P\) represent the original price of the item in dollars. The savings amount corresponds to the discount value, which is \(20\%\) of the original price. Therefore, we can relate these quantities with the equation \(0.20 \times P = 13\).
- Solving for the Original Price
To find the original price \(P\), we need to isolate it in the equation \(0.20 \times P = 13\). We do this by dividing both sides of the equation by \(0.20\):
\[P = \frac{13}{0.20}\]
Performing this division, we have:
\[P = \frac{13}{1/5} = 13 \times 5 = 65\]
Thus, the original price of the item was \(\$65\).
- Conclusion
We have determined that the original price of the item is \(\$65\). To verify, \(20\%\) of \(\$65\) is calculated as \(0.20 \times 65 = 13\), which matches the savings amount mentioned in the problem. The final answer is \(\boxed{\$65}\).
Examples
Understanding percentage discounts is essential for smart shopping. For example, if you see a sale sign at your favorite clothing store, knowing how to quickly calculate the original price from the savings allows you to determine if the deal is truly worth it. This skill helps you manage your budget and make informed financial decisions while shopping for clothes, electronics, or groceries.