**Fiona is serving iced tea and lemonade at a picnic. She has only 44 glasses in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of iced tea she can serve?**

The concepts used in this question are:

- Variables: In algebra, variables are used to represent unknown quantities. In this problem, we have two variables:

- x represents the number of glasses of iced tea
- y represents the number of glasses of lemonade

- Inequalities: Inequalities are mathematical statements that compare two quantities and express that one is greater than, less than, or equal to the other. In this problem, we use an inequality to represent the fact that the total number of glasses cannot exceed 44.
- Solving equations and inequalities: To find the equation that represents the number of glasses of iced tea Fiona can serve, we solve the inequality for x by subtracting y from both sides.
- System of equations: In problems with multiple variables, a system of equations can be used to represent the relationships between the variables. In this problem, we have only one equation (or inequality), so we do not have a system of equations.

By applying these concepts, we were able to find the equation that represents the number of glasses of iced tea Fiona can serve.

**Step-by-Step Explanation:**

**Step 1: Understand the problem **

Fiona is serving iced tea and lemonade at a picnic. She has only 44 glasses in which to serve the drinks. We need to find the equation that represents the number of glasses of iced tea she can serve.

**Step 2: Define the variables **

We are given two variables:

- x represents the number of glasses of iced tea
- y represents the number of glasses of lemonade

**Step 3: Write an inequality to represent the problem**

Since Fiona has only 44 glasses in which to serve the drinks, the total number of glasses cannot exceed 44. We can represent this as an inequality:

x + y ≤ 44

This inequality means that the sum of the number of glasses of iced tea and the number of glasses of lemonade cannot be more than 44.

**Step 4: Solve the inequality for x **

To find the equation that represents the number of glasses of iced tea Fiona can serve, we need to solve the inequality for x. We can do this by subtracting y from both sides:

x ≤ 44 – y

This equation tells us that the number of glasses of iced tea that Fiona can serve is less than or equal to 44 minus the number of glasses of lemonade.

**Step 5: Interpret the result **

The equation x ≤ 44 – y represents the number of glasses of iced tea that Fiona can serve, where x is the number of glasses of iced tea and y is the number of glasses of lemonade.

## Method 2

**Step-by-Step Explanation:**

**Step 1**

We are given that Fiona has 44 glasses total to serve iced tea and lemonade.

**Step 2**

We are told that the number of glasses of iced tea is represented by x, and the number of glasses of lemonade is represented by y.

**Step 3**

The equation we are looking for should represent the number of glasses of iced tea Fiona can serve.

**Step 4**

Since Fiona has a total of 44 glasses and serves both iced tea and lemonade, we can represent the total number of glasses as the sum of the number of glasses of iced tea and the number of glasses of lemonade: x + y = 44.

However, this is not one of the given answer choices.

The only equation that involves x and y and also involves 44 is d) x = 44 – y.

Therefore, **the correct answer is OPTION D i.e x = 44 – y**.

**Let’s take a look at why the other answer choices are incorrect:**

a) x – y = 44: This equation represents the difference between the number of glasses of iced tea and the number of glasses of lemonade. It does not represent the number of glasses of iced tea Fiona serves.

b) 44 + y = x: This equation represents the number of glasses of lemonade that Fiona is serving. It does not represent the number of glasses of iced tea Fiona serves.

c) y – x = 44: This equation represents the difference between the number of glasses of lemonade and the number of glasses of iced tea. It does not represent the number of glasses of iced tea Fiona serves.

**Alternative Method**

**Solution:** Let the number of iced tea glasses be = x

Let the number of lemonade glasses be = y

The total number of glasses is = 44

According to the given data, the equation will be x + y = 44

The number of iced tea glasses is given by x = 44 – y

**Hence, the correct answer is x = 44 – y**

**Conclusion**

**Fiona is serving iced tea and lemonade at a picnic. She has only 44 glasses in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, x=44-y represents the number of glasses of iced tea she can serve.**