Recording-2025-01-09T18:34:14.759Z

Problem Solving Process

• A clear problem-solving process is essential.

Steps of the Process

1. Read the Question

   • Understand what the question is asking and identify the unknowns.

2. Look for Clues

   • Determine what operations you need: add, subtract, multiply, etc.

   • Clues lead to forming a strategy.

3. Choose a Strategy

   • Strategies may vary per problem.

   • Options include creating a table, graph, or equation.

4. Check Your Answer

   • Ensure the solution makes sense in the context of the original question.

Example Problem: Canoe Rental

• A canoe rental company charges a $20 base fee plus $7.50 per hour. Marcy spent a total of $57.50 on the rental.

Question

• For how long did Marcy rent the canoe?

Clues from the Problem

• Base fee: $20

• Cost per hour: $7.50

• Total amount spent: $57.50

Strategy

• Create an equation.

  • Start with the base fee and add the hourly costs:

  • Equation:

    Total Cost = Base Fee + (Cost per Hour × Number of Hours)

  • Let h = number of hours.

  • Therefore, the equation is:

    $57.50 = 20 + 7.50h

Solving the Equation

1. Subtract $20 from both sides:

   • $57.50 - $20 = 7.50h

   • 37.50 = 7.50h

2. Divide both sides by $7.50:

   • h = 37.50 / 7.50

   • h = 5

Checking the Answer

• Insert h = 5 back into the equation:

  • $20 + (7.50 × 5) = $57.50

  • $20 + $37.50 = $57.50

  • The equation holds true.

Conclusion

• Marcy rented the canoe for 5 hours.

• The solution is consistent with the original question.