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.