Let the number of gigabytes of data be $x$.

For Plan A, the total cost is: $C_A = 25 + 10x$ where $25 is the base monthly charge, and $10 per gigabyte of data is the additional charge.

For Plan B, the total cost is: $C_B = 50 + 5x$ where $50 is the base monthly charge, and $5 per gigabyte of data is the additional charge.

To find the number of gigabytes of data where both plans have the same cost, set the equations equal to each other: $25 + 10x = 50 + 5x$

Solve for $x$:

1. Subtract $5x$ from both sides: $25 + 5x = 50$
2. Subtract 25 from both sides: $5x = 25$
3. Divide both sides by 5: $x = 5$

So, the number of gigabytes of data that results in the same cost for one month is 5 gigabytes.

Would you like more details or explanations on this? Here are five questions to consider:

1. What happens if you use more than 5 gigabytes?
2. How does the cost comparison change for different usage levels?
3. Can we generalize this for other monthly base charges?
4. How would the results change if the per-gigabyte cost increased?
5. What would be the total cost for 10 gigabytes under each plan?

Tip: In problems like these, always look for the point where two cost structures intersect to compare them effectively.