Question

2.) tim is choosing between two cell phone plans that offer the same amount of free minutes. at&ts plan charges $39.99 per month with additional minutes costing $0.45. verizons plan costs $44.99 with additional minutes at $0.40. how many additional minutes, a, will it take for the two plans to cost the same? expression 1: ______ expression 2: ____ final answer (number): ____ final answer (sentence): ______

Explanation:

Step1: Set up cost - equations

Let $a$ be the number of additional minutes. The cost of Verizon's plan $C_V$ is $C_V=44.99 + 0.40a$, and the cost of AT&T's plan $C_A$ is $C_A=39.99+0.45a$.

Step2: Set the two cost - equations equal

We want to find when $C_V = C_A$, so $44.99 + 0.40a=39.99 + 0.45a$.

Step3: Solve for $a$

First, subtract $0.40a$ from both sides: $44.99=39.99 + 0.45a-0.40a$. Then simplify to get $44.99=39.99 + 0.05a$. Next, subtract $39.99$ from both sides: $44.99 - 39.99=0.05a$, which gives $5 = 0.05a$. Finally, divide both sides by $0.05$: $a=\frac{5}{0.05}=100$.

Answer:

The number of additional minutes is 100. It will take 100 additional minutes for the two plans to cost the same.