Question

David has a smart phone data plan that costs $30 per month that includes 6 GB of data, but will charge an extra $10 per GB over the included amount. How much would David have to pay in a month where he used 4 GB over the limit? How much would David have to pay in a month where he went over by xx GB?

Answer 1

To calculate David's total cost for using data beyond his plan limit, we can break it down into two parts: the base cost of the plan and the additional cost for the extra data used.

1. The base cost of David's plan is **$30**.
2. The plan includes **6 GB** of data. If David uses more than this, he will be charged an additional **$10 per GB** for the extra data.

### Case 1: Using 4 GB over the limit

- Total data used = 6 GB (included) + 4 GB (over)
- Total data used = 10 GB
- Extra data = 4 GB

Now, calculating the additional cost:
- Extra cost = \( 4 \, \text{GB} \times 10 \, \text{\$ per GB} = 40 \, \text{\$} \)

Now add this to the base cost:
- Total cost = Base cost + Extra cost
- Total cost = 30 \$ + 40 \$ = **70 \$**

### Case 2: Using xx GB over the limit

If David uses "xx" GB over the limit, you can substitute "xx" into the formula:

- Total data used = 6 GB + xx GB
- Extra data = xx GB

Then, the additional cost would be:
- Extra cost = \( xx \, \text{GB} \times 10 \, \text{\$ per GB} = 10 \times xx \, \text{\$} \)

Now adding it to the base cost:
- Total cost = Base cost + Extra cost
- Total cost = \( 30 \, \text{\$} + (10 \times xx) \, \text{\$} \)

So, David would pay:
\[
\text{Total cost} = 30 + 10 \times xx \, \text{\$}
\]

This formula will give David's total payment based on how many GB he goes over the limit.