Cell Phone Plan A charges $25 per month plus $10 per gigabyte of data. Cell Phone Plan B charges $50 per month plus $5 per gigabyte of data. What number of gigabytes of data results in the same cost for one month?

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.

Find out how to compare two cell phone plans using linear equations. In this problem, you'll learn how to set up and solve cost equations to determine the number of gigabytes where both plans have the same cost. Perfect for Grades 6-8.

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