Question

go achète un plateau de fromages et demi pour recevoir des amis à la maison. pure tous les calculs permettant de déterminer le montant payé par hugo. 27,72 ÷ 2 + 27,72 27,72 ÷ 1,5 1,5 × 27,72 27,72 +

Explanation:

Step1: Understand the Problem

Hugo buys 1.5 (one and a half) cheese platters. Let the price of one platter be \( 27.72 \) (currency unit). We need to find the total amount he pays, which is the price of 1.5 platters.

Step2: Analyze Each Expression

- **Expression 1: \( 27.72 \div 2 + 27.72 \)**
This is equivalent to \( \frac{27.72}{2} + 27.72 \), which is the price of half a platter plus the price of one platter (total for 1.5 platters).
- **Expression 2: \( 27.72 \div 1.5 \)**
This would be the price per platter if we divide the total by 1.5, which is not what we need (we need total for 1.5 platters, not price per platter).
- **Expression 3: \( 1.5 \times 27.72 \)**
This directly calculates the total price for 1.5 platters (since \( 1.5 \) is the number of platters and \( 27.72 \) is the price per platter).
- **Expression 4: Incomplete, so we ignore it.**

Now, let's calculate the correct expressions:

Calculating \( 27.72 \div 2 + 27.72 \):

\( 27.72 \div 2 = 13.86 \)
\( 13.86 + 27.72 = 41.58 \) (Wait, but the handwritten answer is \( 6,93\$ \)? Wait, maybe there's a misinterpretation. Wait, maybe the original problem has a different context. Wait, perhaps the price of one platter is not \( 27.72 \), but maybe the total for 4 platters? Wait, no—let's re-examine. Wait, the handwritten answer is \( 6,93\$ \). Let's check \( 27.72 \div 4 = 6.93 \)? No. Wait, maybe the problem is about a platter and a half, but the price per platter is different. Wait, maybe I misread. Wait, the first handwritten answer is \( 6,93\$ \), and the second is \( 0,1254 \). Wait, maybe the original problem is: Hugo buys a platter of cheese and a half, but the price of one platter is \( 27.72 \) cents? No, that seems off. Wait, perhaps the correct expression to get \( 6.93 \) is \( 27.72 \div 4 = 6.93 \)? No. Wait, maybe the problem is that a platter costs \( 27.72 \) for 4 units, and he buys 1.5 units? No, the text says "un plateau de fromages et demi" (one and a half cheese platters).

Wait, maybe the intended calculation is for a different scenario. Wait, let's check the expression that gives \( 6.93 \). Let's compute \( 27.72 \div 4 = 6.93 \), but that's not one of the expressions. Wait, the first expression: \( 27.72 \div 2 + 27.72 = 13.86 + 27.72 = 41.58 \). The third expression: \( 1.5 \times 27.72 = 41.58 \). But the handwritten answer is \( 6,93\$ \). Wait, maybe the price of one platter is \( 27.72 \) divided by 4? No. Wait, maybe the problem is about a different quantity. Wait, perhaps the original problem is: Hugo buys a platter and a half, and the total for 4 platters is \( 27.72 \). Then the price per platter is \( 27.72 \div 4 = 6.93 \), and for 1.5 platters, it's \( 6.93 \times 1.5 = 10.395 \). No. Wait, the handwritten answer is \( 6,93\$ \), which matches \( 27.72 \div 4 = 6.93 \). But that doesn't align with the expressions. Wait, maybe the expressions are for a different calculation. Wait, maybe the problem is to find the price of half a platter? Let's check \( 27.72 \div 4 = 6.93 \). No. Wait, \( 27.72 \div (2 + 2) = 6.93 \)? No. Wait, maybe the first expression is miscalculated. Wait, maybe the correct expression to get \( 6.93 \) is \( 27.72 \div 4 = 6.93 \), but that's not one of the given expressions. Wait, perhaps there's a typo. Alternatively, maybe the original problem has a different price.

Wait, let's re-express the problem. If Hugo buys 1.5 platters, and the price of one platter is \( x \), then total is \( 1.5x \). If the handwritten answer is \( 6.93 \), then \( 1.5x = 6.93 \implies x = 4.62 \). But that doesn't relate to \( 27.72 \). Alternatively, maybe the price of 4 platters is \( 27.72 \), so price per platter is \( 27.72 \div 4 = 6.93 \), and Hugo buys 1 platter: \( 6.93 \). But the problem says "un plateau de fromages et demi" (one and a half platters). So this is confusing.

Wait, maybe the initial handwritten answer is incorrect, or I misread the problem. Let's focus on the expressions. The correct mathematical expressions for "one and a half platters" (1.5 platters) are:

- \( 1.5 \times \text{price per platter} \) (Expression 3: \( 1.5 \times 27.72 \))
- Or \( \text{price of 1 platter} + \text{price of 0.5 platter} = \text{price per platter} + \frac{\text{price per platter}}{2} = \frac{3}{2} \times \text{price per platter} \) (Expression 1: \( 27.72 \div 2 + 27.72 \))

Calculating \( 1.5 \times 27.72 \):
\( 1.5 \times 27.72 = 41.58 \)

Calculating \( 27.72 \div 2 + 27.72 \):
\( 13.86 + 27.72 = 41.58 \)

But the handwritten answer is \( 6,93\$ \), which is \( 27.72 \div 4 = 6.93 \). So perhaps the problem is about a different quantity (e.g., 4 platters, and Hugo buys 1 platter). But the problem states "un plateau de fromages et demi" (one and a half platters). This is conflicting.

Alternatively, maybe the original price is \( 27.72 \) for 4 platters, so price per platter is \( 27.72 \div 4 = 6.93 \), and Hugo buys 1 platter: \( 6.93 \). But the problem says "et demi" (and a half), so that doesn't fit.

Given the confusion, but focusing on the mathematical expressions:

The correct expressions for 1.5 platters (one and a half) are \( 1.5 \times 27.72 \) (Expression 3) or \( 27.72 \div 2 + 27.72 \) (Expression 1), both giving \( 41.58 \). The handwritten answer \( 6,93\$ \) might be a mistake, or perhaps the price per platter is \( 27.72 \div 4 = 6.93 \), but that's not aligned with the problem statement.

Answer:

To determine the amount Hugo pays for 1.5 cheese platters (price per platter = \( 27.72 \)):

• Correct Expressions: \( 1.5 \times 27.72 \) or \( 27.72 \div 2 + 27.72 \)
• Calculation:

\( 1.5 \times 27.72 = 41.58 \) (or \( 27.72 \div 2 + 27.72 = 13.86 + 27.72 = 41.58 \))

(Note: The handwritten answer \( 6,93\$ \) may be incorrect or based on a different interpretation of the problem’s context.)

Final amount paid: \( \boldsymbol{41.58} \) (currency unit, e.g., dollars).