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:
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Assign variables to represent unknown ages:
Let x represent Cristina's age.
Paolo's age is then 2x twiceCristina′sage.
Luca's age is 2x + 3 3yearsmorethanPaolo.
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Set up the equation based on the given information:
x + 2x + 2x+3 = 33
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Solve the equation:
Simplify: 5x + 3 = 33
Subtract 3 from both sides: 5x = 30
Divide both sides by 5: x = 6
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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
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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.
