Carlos invents 50 Geometry problems in 4 days, dedicating 5 hours a day. How many days does he need? to invent 80 problems, if you intend to work on them 2 hours a day?

1. Calculate the number of problems Carlos invents per hour in the initial scenario:
\frac{50}{4 \times 5} = 2.5

2. Determine how many hours it will take to invent 80 problems at the same rate:
\frac{80}{2.5} = 32

3. Calculate how many days are needed if working 2 hours a day:
\frac{32}{2} = 16

Answer: Carlos needs 16 days.