Select The Correct Answer.Three Families Visited The Local Fair Over A Holiday Weekend:- The Rawlins Family Spent $$ 51$ On Admission For 2 Children And 3 Adults, Plus 50 Carnival Tickets.- The Alvarez Family Spent $$

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Introduction

Mathematical problem solving is an essential skill that involves applying mathematical concepts and techniques to solve real-world problems. In this article, we will explore a mathematical problem involving three families who visited the local fair over a holiday weekend. We will use mathematical concepts and techniques to solve the problem and find the correct answer.

The Problem

Three families visited the local fair over a holiday weekend. The Rawlins family spent $51 on admission for 2 children and 3 adults, plus 50 carnival tickets. The Alvarez family spent an unknown amount on admission for 2 children and 3 adults, plus 50 carnival tickets. The Hernandez family spent $75 on admission for 2 children and 3 adults, plus 50 carnival tickets.

Step 1: Define the Variables

Let's define the variables:

  • R = amount spent by the Rawlins family
  • A = amount spent by the Alvarez family
  • H = amount spent by the Hernandez family

We know that R = $51, H = $75, and the number of carnival tickets purchased by each family is 50.

Step 2: Write the Equations

We can write the equations based on the given information:

  • 2x + 3y + 50z = 51 (Rawlins family)
  • 2x + 3y + 50z = A (Alvarez family)
  • 2x + 3y + 50z = 75 (Hernandez family)

where x is the cost of admission for a child, y is the cost of admission for an adult, and z is the cost of a carnival ticket.

Step 3: Solve the System of Equations

We can solve the system of equations using substitution or elimination method. Let's use the substitution method.

From the first equation, we can express x in terms of y and z:

x = (51 - 3y - 50z) / 2

Substituting this expression into the second and third equations, we get:

2(51 - 3y - 50z) / 2 + 3y + 50z = A 2(51 - 3y - 50z) / 2 + 3y + 50z = 75

Simplifying the equations, we get:

51 - 3y - 50z + 3y + 50z = A 51 - 3y - 50z + 3y + 50z = 75

Combine like terms:

51 = A 51 = 75

This is a contradiction, which means that the system of equations has no solution.

Conclusion

The system of equations has no solution, which means that the Alvarez family spent an unknown amount on admission for 2 children and 3 adults, plus 50 carnival tickets. The correct answer is not a specific amount, but rather a statement that the Alvarez family spent an unknown amount.

Final Answer

Q&A: Mathematical Problem Solving

Q: What is mathematical problem solving?

A: Mathematical problem solving is the process of applying mathematical concepts and techniques to solve real-world problems. It involves using mathematical models, equations, and algorithms to analyze and solve problems.

Q: What are the steps involved in mathematical problem solving?

A: The steps involved in mathematical problem solving are:

  1. Define the problem: Clearly define the problem and identify the key elements.
  2. Gather information: Collect relevant data and information about the problem.
  3. Develop a plan: Develop a plan to solve the problem, including the mathematical techniques and tools to be used.
  4. Solve the problem: Use mathematical techniques and tools to solve the problem.
  5. Check the solution: Check the solution to ensure it is correct and valid.

Q: What are some common mathematical techniques used in problem solving?

A: Some common mathematical techniques used in problem solving include:

  1. Algebra: Using variables and equations to solve problems.
  2. Geometry: Using shapes and spatial relationships to solve problems.
  3. Calculus: Using rates of change and accumulation to solve problems.
  4. Statistics: Using data and probability to solve problems.

Q: How can I improve my mathematical problem-solving skills?

A: To improve your mathematical problem-solving skills, try the following:

  1. Practice regularly: Practice solving mathematical problems regularly to develop your skills.
  2. Use online resources: Use online resources, such as Khan Academy and Mathway, to access mathematical problems and solutions.
  3. Join a study group: Join a study group or find a study partner to work on mathematical problems together.
  4. Seek help when needed: Don't be afraid to seek help when you need it. Ask your teacher or a tutor for assistance.

Q: What are some common mistakes to avoid when solving mathematical problems?

A: Some common mistakes to avoid when solving mathematical problems include:

  1. Not reading the problem carefully: Make sure to read the problem carefully and understand what is being asked.
  2. Not using the correct mathematical techniques: Use the correct mathematical techniques and tools to solve the problem.
  3. Not checking the solution: Check the solution to ensure it is correct and valid.
  4. Not seeking help when needed: Don't be afraid to seek help when you need it.

Q: How can I apply mathematical problem-solving skills to real-world problems?

A: Mathematical problem-solving skills can be applied to a wide range of real-world problems, including:

  1. Business: Using mathematical techniques to analyze and solve business problems.
  2. Science: Using mathematical techniques to analyze and solve scientific problems.
  3. Engineering: Using mathematical techniques to design and solve engineering problems.
  4. Finance: Using mathematical techniques to analyze and solve financial problems.

Conclusion

Mathematical problem solving is an essential skill that involves applying mathematical concepts and techniques to solve real-world problems. By following the steps involved in mathematical problem solving and using the correct mathematical techniques, you can improve your mathematical problem-solving skills and apply them to a wide range of real-world problems.

Final Answer

The final answer is: Mathematical problem solving is a valuable skill that can be applied to a wide range of real-world problems.