At a special sale, 5 tickets can be purchased for the price of 3 tickets. If 5 tickets are purchased at the sale, the amount saved will be what percent of the original price of the 5 tickets?

### Concept & Formula This is a classic discount problem. The percentage saved (discount percentage) is calculated based on the original price of the items obtained, not the price paid. $$ \text{Percentage Saved} = \left( \frac{\text{Amount Saved}}{\text{Original Price}} \right) \times 100 $$ ### Step-by-Step Solution * Let the original price of $1$ ticket be $P$. * The original price for $5$ tickets would be $5P$. * The customer pays the price of $3$ tickets to get $5$ tickets. So, the amount paid is $3P$. * The amount saved is the difference between the original price and the amount paid: $5P - 3P = 2P$. * The percentage saved is calculated over the original price of the $5$ tickets ($5P$). * $$\text{Percentage Saved} = \left( \frac{2P}{5P} \right) \times 100 = \frac{2}{5} \times 100 = 40\%$$ ### Exam Strategy & Shortcut **Direct Ratio Method:** Think in terms of tickets instead of money. You are getting $5$ tickets but only paying for $3$. That means you get $2$ tickets completely free. The savings is simply $2$ free tickets out of a total original value of $5$ tickets. $$\frac{2}{5} = 40\%$$ You can solve this mentally in seconds without variables. ### Common Pitfall Students often calculate the savings percentage relative to the amount they paid (the price of $3$ tickets), yielding $\frac{2}{3} = 33.33\%$. Remember, discounts and savings are always calculated on the **original/marked price** unless stated otherwise. ### Final Answer **Therefore, the correct answer is 40%.**