Solving Age Problems with First-Degree Equations

This page presents a detailed walkthrough of solving a complex age-related problem using first-degree equations, demonstrating the practical application of problemi risolvibili con equazioni di primo grado.

The problem statement introduces three brothers - Luca, Paolo, and Cristina - and provides information about their ages:

• The sum of their ages is 33 years.
• Luca is 3 years older than Paolo.
• Paolo is twice as old as Cristina.

To solve this problem, we follow these steps:

1. Assign variables to represent unknown ages:

   • Let x represent Cristina's age.
   • Paolo's age is then 2x (twice Cristina's age).
   • Luca's age is 2x + 3 (3 years more than Paolo).

2. Set up the equation based on the given information: x + 2x + $2x + 3$ = 33

3. Solve the equation:

   • Simplify: 5x + 3 = 33
   • Subtract 3 from both sides: 5x = 30
   • Divide both sides by 5: x = 6

4. Calculate the ages of all three siblings:

   • Cristina: x = 6 years old
   • Paolo: 2x = 2 * 6 = 12 years old
   • Luca: 2x + 3 = $2 * 6$ + 3 = 15 years old

5. Verify the solution by checking if it satisfies all given conditions.

Example: This problem demonstrates how to use equazioni di primo grado to solve real-world age-related questions, a common application in problemi risolvibili con equazioni di primo grado scuola media.

Highlight: The key to solving such problems is to correctly set up the equations based on the given relationships between the unknowns.

Vocabulary: "Equazione di 1° grado" refers to a first-degree equation, which is a linear equation involving one unknown variable raised to the first power.

This method of problem-solving is particularly useful for students learning equazioni di primo grado esercizi zanichelli and can be applied to various problemi con equazioni di primo grado scenarios.