The uploaded document contains a variety of mathematical problems related to systems of equations, affine functions, and real-life applications. Below is a summary and possible starting points for solving these types of problems:

Systems of Equations:

1. Raúl's Banknotes:

   • Variables: Number of 50 and 100 S/. bills.
   • Equations:
     1. $x + y = 45$ (total number of bills)
     2. $50x + 100y = 3500$ (total value of the bills).

2. Cine and Teatro Visits:

   • Variables: Number of visits to the cinema and the theater.
   • Equations:
     1. $x + y = 20$ (total outings)
     2. $15x + 25y = 360$ (total money spent).

3. Father's Problem Challenge:

   • Variables: Correct and incorrect solutions.
   • Equations:
     1. $x + y = 12$ (total problems)
     2. $10x - 6y = 72$ (total earnings).

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Affine Functions:

1. Evaluating Functions:

   • Calculate values like $f(x) = 3x + 5$ for specific inputs.

2. Operations with Functions:

   • Example: $f(x) = 7x + 2$, calculate $f(-8) + f(-3) + f(5)$.

3. Finding Functions:

   • Example sequence: $5, 8, 11, 14, 17$. Identify the linear rule $f(x) = 3x + 2$.

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Real-Life Scenarios with Functions:

1. Sales Commissions:

   • $f(x) = 40 + 15x$, find income for 12 sales.

2. Business Earnings:

   • Sequence earnings: $12, 24, 36$, derive total earnings for April.

3. Service Costs:

   • Grúa: $f(x) = 40 + 70x$. Solve for $x$ under $f(x) \leq 600$.

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Follow-up Questions:

1. Do you want help solving a specific system of equations in the document?
2. Shall we analyze any particular affine function or sequence for its formula?
3. Would you like practical guidance on the real-life scenarios involving functions?
4. Are you interested in graphical interpretations of any of these problems?
5. Should I provide general strategies for solving systems of equations or affine functions?

Tip:

When solving systems of equations, start by simplifying one equation to express one variable in terms of the other. Substitute this expression into the other equation to reduce the system.