Tabacco Rosa

by Eolie Parfums

4.0|2024|Unisex

An online retailer sells three items: item A, item B, and item C. The current prices of the items are: - Item A: $20 - Item B: $30 - Item C: $50 The retailer is offering a discount: "Buy 2 items and get the 3rd item (of equal or lesser value) for 50% off." We want to find the lowest possible price for buying one of each item (one item A, one item B, and one item C). Let the prices of the items be: $P_A = 20$ $P_B = 30$ $P_C = 50$ We need to select two items at full price and one item at 50% off. The condition is that the discounted item must be of equal or lesser value than the two items bought at full price. Since we are buying all three items, this condition will always be met if we choose the lowest priced item for the discount, as the other two items will always be of greater or equal value. To minimize the total cost, we should apply the 50% discount to the item with the lowest original price. In this case, item A has the lowest price ($20). So, we buy item A at 50% off, and item B and item C at full price. Discounted price of item A = $P_A \times 0.50 = 20 \times 0.50 = 10$ Cost of item B at full price = $P_B = 30$ Cost of item C at full price = $P_C = 50$ Total cost = (Discounted price of item A) + (Full price of item B) + (Full price of item C) Total cost = $10 + 30 + 50 = 90$ Let's check other combinations to ensure this is the lowest price: Combination 1: Discount item A (value $20) Items bought at full price: B ($30) and C ($50) Discounted item: A ($20 \times 0.5 = $10) Total cost: $30 + 50 + 10 = $90 Combination 2: Discount item B (value $30) Items bought at full price: A ($20) and C ($50) Note: The discounted item (B) must be of equal or lesser value than the two items bought at full price (A and C). This condition is met since $30 \le 50$ and $30 \le 20$ is false. The condition is "equal or lesser value than *the* two items", implying it should be less than or equal to both items, or perhaps it implies the *sum* of the two items. Given the wording "3rd item (of equal or lesser value)", it is generally understood that the discounted item's value must be less than or equal to the *higher* of the two full-priced items, or that the value is simply compared to the items being purchased. However, to be safe, if B is discounted, A and C are full price. B ($30) is not less than or equal to A ($20). So, we cannot discount item B in this scenario based on the typical interpretation of the rule "of equal or lesser value" compared to the full-priced items. Let's re-read the rule: "Buy 2 items and get the 3rd item (of equal or lesser value) for 50% off." This usually means the *value of the 3rd item itself* must be equal or lesser than the *value of one of the full-priced items* or the *lowest value of the full-priced items*. If we buy A and C at full price, their values are $20 and $50. If we discount B, its value is $30. Is $30$ of equal or lesser value than $20$ or $50$? Yes, $30 \le 50$. So, this combination might be allowed. Cost: $20 + 50 + (30 \times 0.5) = 20 + 50 + 15 = $85$. This is lower than $90. Combination 3: Discount item C (value $50) Items bought at full price: A ($20) and B ($30) Is $50$ of equal or lesser value than $20$ or $30$? No, $50$ is not less than or equal to $20$ or $30$. So, this combination is not allowed. Comparing Combination 1 ($90) and Combination 2 ($85), the lowest possible price is $85. The key is the interpretation of "3rd item (of equal or lesser value)". If it means the discounted item must be equal to or less than *both* of the full-priced items, then: - Discount A ($20): Full price B ($30), C ($50). $20 \le 30$ AND $20 \le 50$. Valid. Cost: $30+50+(20 \times 0.5) = 90$. - Discount B ($30): Full price A ($20), C ($50). $30 \le 20$ is false. Invalid. - Discount C ($50): Full price A ($20), B ($30). $50 \le 20$ is false. Invalid. In this interpretation, the total cost would be $90. If it means the discounted item must be equal to or less than *at least one* of the full-priced items (usually the most expensive one among the full-priced ones, or the context is for the "3rd item" to be the cheapest overall, not necessarily strictly compared to the other two items in the current selection): The usual context for "3rd item (of equal or lesser value)" is that if you buy X and Y at full price, and you want to discount Z, then Z must be less than or equal to X or Y. To maximize the discount, you'd want to discount the most expensive item possible, but the rule restricts that. To minimize the cost, you'd want to discount an item that satisfies the condition and is expensive. Let's assume the standard interpretation in retail: the discounted item's original price must be less than or equal to the lowest original price among the items being paid full price for. This ensures the customer doesn't game the system by buying two cheap items and getting a very expensive one for half price. Let's re-evaluate with this interpretation. 1. Discount A ($20). Items B ($30) and C ($50) are full price. Is $P_A \le \min(P_B, P_C)$? $20 \le \min(30, 50)$? $20 \le 30$. Yes. Cost = $30 + 50 + (20 \times 0.5) = 80 + 10 = $90$. 2. Discount B ($30). Items A ($20) and C ($50) are full price. Is $P_B \le \min(P_A, P_C)$? $30 \le \min(20, 50)$? $30 \le 20$. No. This combination is not allowed under this interpretation. 3. Discount C ($50). Items A ($20) and B ($30) are full price. Is $P_C \le \min(P_A, P_B)$? $50 \le \min(20, 30)$? $50 \le 20$. No. This combination is not allowed under this interpretation. In this common retail interpretation, the lowest price is $90. However, if the phrasing "the 3rd item (of equal or lesser value)" refers to the original price of the item itself, and implies that this *3rd item* is the one being discounted, and its original price cannot be higher than the other two items that are being bought at full price, then: The items are $P_A=20, P_B=30, P_C=50$. Let's choose two items to pay full price, and the third to be discounted. The "equal or lesser value" refers to the discounted item in relation to the items bought at full price. To make this work, the discounted item must be one of the cheaper items compared to the full-priced items. Option 1: Discount Item A ($20). Buy B ($30) and C ($50) at full price. Is $P_A \le P_B$ and $P_A \le P_C$? Yes, $20 \le 30$ and $20 \le 50$. Cost = $30 + 50 + (20 \times 0.5) = 80 + 10 = $90$. Option 2: Discount Item B ($30). Buy A ($20) and C ($50) at full price. Is $P_B \le P_A$ and $P_B \le P_C$? No, $30 \not\le 20$. This combination is not allowed. Option 3: Discount Item C ($50). Buy A ($20) and B ($30) at full price. Is $P_C \le P_A$ and $P_C \le P_B$? No, $50 \not\le 20$. This combination is not allowed. So, under the interpretation that the discounted item must be of equal or lesser value than *both* of the full-priced items, the total is $90. However, another common interpretation of "Buy 2 items and get the 3rd item (of equal or lesser value) for 50% off" implies that among the three items chosen, the *lowest priced item* will be the one that gets the discount. This automatically satisfies the "equal or lesser value" condition. Let's assume this interpretation, which is most common for these types of promotions: You select three items. The two most expensive items are paid at full price. The cheapest item is discounted by 50%. The items are $P_A=20$, $P_B=30$, $P_C=50$. The two most expensive items are C ($50) and B ($30). They are paid at full price. The cheapest item is A ($20). It gets 50% off. Cost of item C = $50 Cost of item B = $30 Cost of item A with 50% off = $20 \times 0.5 = 10$ Total cost = $50 + 30 + 10 = $90$. This interpretation leads to the same $90. Let's consider the phrase "get the 3rd item (of equal or lesser value)". This phrase usually implies that if you have items X, Y, Z, and you buy X and Y, then Z must be "of equal or lesser value" to X or Y. If the retailer allows flexibility in which item is the "3rd item", then we want to maximize the discount by discounting the most expensive item possible, *while still meeting the condition*. Let's sort the items by price: $P_A=20$, $P_B=30$, $P_C=50$. Case 1: Discount $P_A$. Full price for