Question

The table shows the relationship between the cost of monthly cell phone Plan A and the number of minutes used within a month. The equation c=30+ 0.10m describes the relationships for the cost c in dollars for minutes m used for Plan B. What is the difference, in dollars, of the total costs of the cell phone plans if a customer talks for 20 minutes?



Time(min) | Cost ($)
0. | 35.00
2. | 35.10
4. | 35.20

Answer 1

To find the difference in the total costs of the two cell phone plans when a customer talks for 20 minutes, we need to determine the total cost for both Plan A and Plan B at 20 minutes.

1. **Calculate the cost for Plan A:**
From the table provided for Plan A, we can observe the pattern based on the given costs for the minutes used. It looks like the cost increases by $0.10 for every 2 minutes.

- When “m = 0”, cost = $35.00
- When “m = 2”, cost = $35.10
- When “m = 4”, cost = $35.20

It's evident that for every 2 minutes, the cost increases by $0.10, which translates to an increase of $0.05 per minute.

Thus, we can write a rule:
\[
\text{Cost for Plan A} = 35 + (0.05 \times m)
\]

For 20 minutes:
\[
\text{Cost for Plan A} = 35 + (0.05 \times 20) = 35 + 1.00 = 36.00
\]

2. **Calculate the cost for Plan B:**
The relationship for Plan B is given by the equation:
\[
c = 30 + 0.10m
\]

For 20 minutes:
\[
c = 30 + (0.10 \times 20) = 30 + 2.00 = 32.00
\]

3. **Calculate the difference in costs:**
Now we find the difference between the costs of Plan A and Plan B.
\[
\text{Difference} = \text{Cost of Plan A} - \text{Cost of Plan B} = 36.00 - 32.00 = 4.00
\]

Therefore, the difference in the total costs of the cell phone plans if a customer talks for 20 minutes is **$4.00**.