Angelo Has $$50$ To Spend On Drinks For His Super Bowl Party. Bottles Of Pepsi Cost $$ 2.75 2.75 2.75 [/tex] Each, And Cans Of Sprite Cost $$2.50$ Each. If $p$ Is The Number Of Bottles Of Pepsi And

Angelo's Super Bowl Party Drinks: A Mathematical Conundrum

Angelo is hosting a Super Bowl party and has a budget of $50 to spend on drinks for his guests. He has two options: bottles of Pepsi that cost $2.75 each and cans of Sprite that cost $2.50 each. The question is, how many bottles of Pepsi and cans of Sprite can Angelo buy with his $50 budget? In this article, we will explore the mathematical solution to this problem and provide a step-by-step guide on how to determine the optimal combination of drinks that Angelo can purchase.

Let's denote the number of bottles of Pepsi as p and the number of cans of Sprite as s. We know that each bottle of Pepsi costs $2.75 and each can of Sprite costs $2.50. Angelo's budget is $50, so we can set up the following equation:

2.75p + 2.50s = 50

Our goal is to find the values of p and s that satisfy this equation.

To solve this equation, we can use the method of substitution or elimination. Let's use the substitution method. We can start by isolating one of the variables, say p. We can do this by subtracting 2.50s from both sides of the equation:

2.75p = 50 - 2.50s

Next, we can divide both sides of the equation by 2.75 to solve for p:

p = (50 - 2.50s) / 2.75

Now that we have an expression for p, we can substitute this expression into the original equation:

2.75((50 - 2.50s) / 2.75) + 2.50s = 50

Simplifying this equation, we get:

50 - 2.50s + 2.50s = 50

This equation is true for all values of s, so we can conclude that s is a free variable. This means that Angelo can buy any number of cans of Sprite as long as he stays within his budget.

Since s is a free variable, we can choose any value for s that we like. Let's choose a value for s and see how many bottles of Pepsi Angelo can buy. Suppose Angelo wants to buy 10 cans of Sprite. In this case, s = 10, and we can substitute this value into the expression for p:

p = (50 - 2.50(10)) / 2.75 p = (50 - 25) / 2.75 p = 25 / 2.75 p = 9.09

Since Angelo can't buy a fraction of a bottle of Pepsi, we round down to the nearest whole number. In this case, Angelo can buy 9 bottles of Pepsi.

In this article, we solved a mathematical problem involving Angelo's Super Bowl party drinks. We set up an equation to represent the situation and used the substitution method to solve for the number of bottles of Pepsi and cans of Sprite that Angelo can buy. We found that s is a free variable, which means that Angelo can buy any number of cans of Sprite as long as he stays within his budget. We also found that Angelo can buy 9 bottles of Pepsi if he wants to buy 10 cans of Sprite.

To find the optimal solution, we need to maximize the number of drinks that Angelo can buy. Let's use the expression for p to find the maximum value of p:

p = (50 - 2.50s) / 2.75

To maximize p, we need to minimize s. Since s is a free variable, we can choose any value for s that we like. Let's choose the smallest possible value for s, which is s = 0. In this case, p = (50 - 2.50(0)) / 2.75 = 50 / 2.75 = 18.18. Since Angelo can't buy a fraction of a bottle of Pepsi, we round down to the nearest whole number. In this case, Angelo can buy 18 bottles of Pepsi.

Now that we have found the optimal solution, we can calculate the total cost of the drinks. The total cost is the sum of the cost of the bottles of Pepsi and the cost of the cans of Sprite:

Total Cost = 2.75p + 2.50s = 2.75(18) + 2.50(0) = 49.50

Since Angelo's budget is $50, he can afford to buy 18 bottles of Pepsi and 0 cans of Sprite.

In this article, we solved a mathematical problem involving Angelo's Super Bowl party drinks. We set up an equation to represent the situation and used the substitution method to solve for the number of bottles of Pepsi and cans of Sprite that Angelo can buy. We found that s is a free variable, which means that Angelo can buy any number of cans of Sprite as long as he stays within his budget. We also found that Angelo can buy 18 bottles of Pepsi if he wants to buy 0 cans of Sprite. The total cost of the drinks is $49.50, which is within Angelo's budget of $50.

The final answer is that Angelo can buy 18 bottles of Pepsi and 0 cans of Sprite with his $50 budget.
Angelo's Super Bowl Party Drinks: A Mathematical Conundrum - Q&A

In our previous article, we solved a mathematical problem involving Angelo's Super Bowl party drinks. We set up an equation to represent the situation and used the substitution method to solve for the number of bottles of Pepsi and cans of Sprite that Angelo can buy. In this article, we will answer some frequently asked questions about the problem and provide additional insights.

Q: What is the optimal solution to the problem?

A: The optimal solution is to buy 18 bottles of Pepsi and 0 cans of Sprite. This combination maximizes the number of drinks that Angelo can buy while staying within his budget of $50.

Q: Why is s a free variable?

A: s is a free variable because the equation 2.75p + 2.50s = 50 can be satisfied for any value of s. This means that Angelo can buy any number of cans of Sprite as long as he stays within his budget.

Q: How can I find the maximum value of p?

A: To find the maximum value of p, you need to minimize s. Since s is a free variable, you can choose any value for s that you like. The smallest possible value for s is s = 0, which gives you the maximum value of p.

Q: What is the total cost of the drinks?

A: The total cost of the drinks is the sum of the cost of the bottles of Pepsi and the cost of the cans of Sprite. In the optimal solution, the total cost is $49.50.

Q: Can I buy a fraction of a bottle of Pepsi?

A: No, you cannot buy a fraction of a bottle of Pepsi. Since Angelo can't buy a fraction of a bottle of Pepsi, we round down to the nearest whole number. In the optimal solution, Angelo can buy 18 bottles of Pepsi.

Q: What if I want to buy a different number of cans of Sprite?

A: If you want to buy a different number of cans of Sprite, you can substitute that value into the expression for p and solve for p. For example, if you want to buy 10 cans of Sprite, you can substitute s = 10 into the expression for p and solve for p.

Q: Can I use a different method to solve the problem?

A: Yes, you can use a different method to solve the problem. For example, you can use the elimination method or the substitution method. The substitution method is used in this article, but you can use any method that you prefer.

In this article, we answered some frequently asked questions about the problem and provided additional insights. We hope that this article has been helpful in understanding the problem and its solution.

If you want to learn more about the problem and its solution, you can check out the following resources:

• The original article: "Angelo's Super Bowl Party Drinks: A Mathematical Conundrum"
• The solution to the problem: "Solving the Equation"
• The optimal solution: "Optimal Solution"
• The total cost of the drinks: "Total Cost"

We hope that this article has been helpful in understanding the problem and its solution. If you have any further questions, please don't hesitate to ask.