Calculating Total Expenses Which Expression Fits

Hey everyone! Let's dive into this math problem that asks us to figure out the best way to calculate how much three friends spent on tickets, food, and drinks. We've got four different expressions to choose from, and we need to break them down to see which one makes the most sense. So, grab your thinking caps, and let's get started!

Understanding the Problem

Before we jump into the expressions, let's make sure we fully understand the situation. We have three friends who are spending money on a few things:

• Tickets: Each friend buys a ticket.
• Food: They share some food.
• Drinks: They also share some drinks.

Our goal is to find a single expression that accurately calculates the total amount of money spent by all three friends. This means we need to consider the cost per item and how many items each person bought or shared.

The key here is to identify the operations we need to perform. We'll likely be using both multiplication (to find the total cost of multiple items) and addition (to combine the costs of different items). We also need to pay attention to the order of operations, which is where those parentheses come in handy!

Now, let's look at the different expressions and see how they stack up.

Analyzing the Expressions

We have four expressions to consider, each using a combination of multiplication, addition, and parentheses. Let's break down each one step-by-step to see what it represents and whether it makes sense in the context of our problem.

Option A: $(3 imes 5) imes (5 + 3 + 6)$

This expression looks a bit complex, so let's tackle it piece by piece.

• (3 × 5): This part seems to be multiplying two numbers. Let's assume '3' represents the number of friends and '5' represents the cost of a ticket. So, this could be the total cost of tickets for all three friends.
• (5 + 3 + 6): This part is adding three numbers together. These numbers likely represent the costs of the food and drinks. Let's assume '5' is the cost of the food, '3' is the cost of one type of drink, and '6' is the cost of another type of drink. So, this sum represents the total cost of food and drinks.
• × (multiplication between the two parentheses): The expression is multiplying the total cost of tickets by the total cost of food and drinks. Now, here's where things get tricky. Multiplying these two totals doesn't really make sense in our scenario. We want to add the cost of tickets to the cost of food and drinks, not multiply them.

So, while the individual parts of this expression might represent something relevant, the overall operation of multiplying the two totals doesn't align with our goal of finding the total spending. This expression is unlikely to be correct.

Option B: $(3 + 5) imes (5 + 3 + 6)$

Let's break down option B in a similar way:

• (3 + 5): Again, let's assume '3' represents the number of friends. But what does '5' represent here? If '5' is the cost of a ticket, then this part is adding the number of friends to the cost of a ticket. This doesn't have a clear meaning in our context. We usually don't add quantities like the number of people and the price of an item.
• (5 + 3 + 6): As before, this part likely represents the total cost of food and drinks, with '5' being the cost of food, '3' the cost of one drink, and '6' the cost of another drink.
• × (multiplication between the two parentheses): This expression is multiplying the sum of (number of friends + ticket cost) by the total cost of food and drinks. This doesn't make much logical sense in our problem. We're looking to combine costs, not multiply seemingly unrelated quantities.

Because the first part of this expression doesn't have a clear meaning, and the overall operation is multiplying sums that don't logically connect, this option is also unlikely to be correct.

Option C: $(3 + 5) + (5 imes 3 imes 6)$

Let's analyze option C:

• (3 + 5): Similar to option B, this part adds the number of friends ('3') to a cost ('5'). If '5' is the cost of a ticket, adding it to the number of friends doesn't have a clear meaning in our scenario. This raises a red flag.
• (5 × 3 × 6): This part multiplies three numbers together. Let's think about what these could represent. If '5' is the cost of food, '3' is the number of friends, and '6' is the cost of a drink per person, then this multiplication might be trying to calculate the total cost of food and drinks. However, the costs of food and drinks are being multiplied by each other as well, which doesn't seem right.
• + (addition between the two parentheses): This expression adds the result of (3 + 5) to the result of (5 × 3 × 6). Since the first part doesn't make logical sense and the second part has a multiplication issue, the overall expression is flawed.

Due to the illogical addition in the first part and the problematic multiplication in the second part, option C is unlikely to be the correct answer.

Option D: $(3 imes 5) + (5 + 3 + 6)$

Now, let's examine option D:

• (3 × 5): As we discussed in option A, if '3' represents the number of friends and '5' represents the cost of a ticket, then this part correctly calculates the total cost of tickets for all three friends.
• (5 + 3 + 6): Like in previous options, this part likely represents the total cost of food and drinks, where '5' is the cost of food, '3' is the cost of one drink, and '6' is the cost of another drink.
• + (addition between the two parentheses): This expression adds the total cost of tickets to the total cost of food and drinks. This is exactly what we need to do to find the total spending by all three friends!

This expression logically combines the cost of tickets with the cost of food and drinks. Therefore, option D appears to be the correct answer.

Conclusion

After carefully analyzing each expression, we've determined that option D, $(3 imes 5) + (5 + 3 + 6)$, is the most likely to correctly calculate the total amount of money spent by the three friends. This expression breaks down the problem into logical steps: first, calculate the total cost of the tickets, then calculate the total cost of food and drinks, and finally, add those two totals together.

So, there you have it! We've successfully navigated this mathematical expression and found the solution. Remember, breaking down complex problems into smaller, more manageable steps is a key strategy in math and in life!