Question

Tim is choosing between two cell phone plans that offer the same amount of free minutes. Cingular’s plan charges $30.00 per month with additional minutes costing $2.00. Verizon’s plan costs $45.00 with additional minutes at $1.00. How many additional minutes, a, will it take for the two plans to cost the same?

Answer 1

To determine the number of additional minutes, \( a \), at which Cingular's and Verizon's plans will cost the same, we can set up an equation based on the cost of each plan.

1. Cingular's plan:
- Monthly fee: $30.00
- Cost for additional minutes: $2.00 per minute
- Total cost for \( a \) additional minutes:
\[
\text{Cost}_{\text{Cingular}} = 30 + 2a
\]

2. Verizon's plan:
- Monthly fee: $45.00
- Cost for additional minutes: $1.00 per minute
- Total cost for \( a \) additional minutes:
\[
\text{Cost}_{\text{Verizon}} = 45 + 1a
\]

Next, we want to find when these two costs are equal:
\[
30 + 2a = 45 + 1a
\]

Now, we can solve the equation for \( a \):
1. Subtract \( 1a \) from both sides:
\[
30 + 2a - 1a = 45
\]
Simplifying gives:
\[
30 + a = 45
\]

2. Subtract 30 from both sides:
\[
a = 45 - 30
\]
Therefore, we find:
\[
a = 15
\]

The number of additional minutes, \( a \), that will make the two plans cost the same is \( \boxed{15} \).