Company A charges $20.40 monthly for up to 3 gigabytes of data and $9.80 per additional gigabyte. Company B charges $18.60 monthly for up to 3 gigabytes of data and $10.10 per additional gigabyte. For what number of additional gigabytes would the two companies charge the same amount?


Let $ x $ represent the number of additional gigabytes used beyond the initial 3 gigabytes.

### Company A:
- Monthly base charge: \$20.40
- Additional charge: \$9.80 per gigabyte

The total cost for Company A is:
\[
C_A(x) = 20.40 + 9.80x
\]

### Company B:
- Monthly base charge: \$18.60
- Additional charge: \$10.10 per gigabyte

The total cost for Company B is:
\[
C_B(x) = 18.60 + 10.10x
\]

To find the number of additional gigabytes where the companies charge the same, set the two cost equations equal to each other:
\[
20.40 + 9.80x = 18.60 + 10.10x
\]

### Solving for $ x $:
1. Subtract 9.80x from both sides:
\[
20.40 = 18.60 + 0.30x
\]

2. Subtract 18.60 from both sides:
\[
1.80 = 0.30x
\]

3. Divide both sides by 0.30:
\[
x = \frac{1.80}{0.30} = 6
\]

Thus, the two companies will charge the same amount when 6 additional gigabytes are used.

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. What would the total cost be for 6 additional gigabytes with either company?
2. How many gigabytes total are being used if there are 6 additional gigabytes?
3. How does the cost comparison change if 7 additional gigabytes are used?
4. What is the cost difference between the two companies for just 1 additional gigabyte?
5. How much more does Company B charge than Company A for 5 additional gigabytes?

**Tip:** In problems like these, always start by setting up clear equations for both companies.

Company A charges $20.40 monthly for up to 3 gigabytes of data and $9.80 per additional gigabyte. Company B charges $18.60 monthly for up to 3 gigabytes of data and $10.10 per additional gigabyte. For what number of additional gigabytes would the two companies charge the same amount?

Solve the problem of comparing data plans from Company A and Company B by setting up linear equations. Discover how many additional gigabytes are needed for both companies to charge the same amount. This problem highlights key algebraic concepts and is suitable for students in Grades 6-8.

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