Question

The following data table represents the total cost of a monthly cell phone bill as a function of the number of minutes that the phone is used each month.

Minutes 500 750 1,000 1,250 1,500
Total Monthly Cost (in dollars) $62 $77 $92 $107 $122
The table shows that as more minutes are used each month, the total monthly cost will increase at the same rate. Assuming that this is true, what is the total monthly cost for the cell phone if it is used for 2,500 minutes?

Answer 1

To find the total monthly cost for the cell phone if it is used for 2,500 minutes, we first need to determine the rate of increase in the total monthly cost per minute used.

From the table provided, we can calculate the cost per block of 250 minutes:

- From 500 to 750 minutes: \(77 - 62 = 15\) dollars
- From 750 to 1,000 minutes: \(92 - 77 = 15\) dollars
- From 1,000 to 1,250 minutes: \(107 - 92 = 15\) dollars
- From 1,250 to 1,500 minutes: \(122 - 107 = 15\) dollars

We see that the cost increases by $15 for every additional 250 minutes.

Next, we need to calculate how many 250-minute blocks are in 2,500 minutes:

\[
\text{Number of 250-minute blocks} = \frac{2500}{250} = 10
\]

Now we need to determine the total increase in cost for these 10 blocks:

\[
\text{Total increase in cost} = 10 \times 15 = 150 \text{ dollars}
\]

Now we add this total increase to the cost at 1,500 minutes:

\[
\text{Total monthly cost for 2,500 minutes} = 122 + 150 = 272 \text{ dollars}
\]

Therefore, the total monthly cost for the cell phone if it is used for 2,500 minutes is **$272**.