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 $ x $ represent the number of gigabytes of data used in a month.

The cost for Plan A is given by:

\[
\text{Cost for Plan A} = 25 + 10x
\]

The cost for Plan B is given by:

\[
\text{Cost for Plan B} = 50 + 5x
\]

To find the number of gigabytes that results in the same cost for both plans, set the two expressions equal to each other:

\[
25 + 10x = 50 + 5x
\]

Now 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:

\[
x = 5
\]

Thus, 5 gigabytes of data will result in the same cost for both plans.

Would you like further details or clarifications?

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Here are 5 related questions to explore:

1. How much would Plan A cost for 7 gigabytes of data?
2. At what point does Plan B become cheaper than Plan A?
3. What would the total monthly cost be for 3 gigabytes of data on Plan B?
4. How can you generalize this problem for any pair of linear pricing plans?
5. What happens if the monthly base fee for Plan A changes?

**Tip:** When solving equations involving costs, always keep track of fixed and variable components separately.

Explore how to solve a linear equation to find the number of gigabytes that equalizes the monthly cost of two different cell phone plans. Learn key algebra concepts, such as cost comparison, variable solving, and equation balancing, suitable for Grades 6-8 students.

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