Joshua pays $125 plus $0.75 for every gigabyte over 5 gigs for his cell phone plan. Jessica pays $150 plus $0.45 for every gigabyte over 5 gigs for her cell phone plan. Write a system of equations to represent this situation where x represent the number of gigabytes over 5 gigs and y represents the total cost of the phone bill

We can model this situation with a system of equations for both Joshua and Jessica, where:

- $ x $ represents the number of gigabytes over 5 gigs.
- $ y $ represents the total cost of the phone bill.

### For Joshua:
Joshua pays a base fee of $125, and an additional $0.75 for every gigabyte over 5 gigs. This can be represented by the equation:
\[
y = 125 + 0.75x
\]

### For Jessica:
Jessica pays a base fee of $150, and an additional $0.45 for every gigabyte over 5 gigs. This can be represented by the equation:
\[
y = 150 + 0.45x
\]

### System of Equations:
\[
\begin{aligned}
y &= 125 + 0.75x \quad \text{(Joshua's equation)} \\
y &= 150 + 0.45x \quad \text{(Jessica's equation)}
\end{aligned}
\]

Would you like to solve or analyze this system further?

### Related Questions:
1. At how many gigabytes over 5 gigs would both bills cost the same?
2. How much would Joshua pay if he used 8 gigabytes over the limit?
3. How much would Jessica pay if she used 10 gigabytes over the limit?
4. How does the cost change for both if they exceed 10 gigabytes?
5. Which plan is more cost-effective for higher data usage?

### Tip:
Identifying the base cost and rate per unit is a key step in forming linear equations from word problems.

Joshua pays $125 plus $0.75 for every gigabyte over 5 gigs for his cell phone plan. Jessica pays $150 plus $0.45 for every gigabyte over 5 gigs for her cell phone plan. Write a system of equations to represent this situation where x represents the number of gigabytes over 5 gigs and y represents the total cost of the phone bill.

Explore how to model cell phone plan costs using a system of linear equations. Joshua's plan charges $125 plus $0.75 for every gigabyte over 5 gigs, while Jessica's plan charges $150 plus $0.45 per gigabyte over 5 gigs. This example demonstrates linear equations and cost functions, suitable for Grades 8-10 students.

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