Question

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 for each plan

Let $a$ be the number of additional minutes. The cost of AT&T's plan, $C_1$, is $C_1 = 39.99+0.45a$. The cost of Verizon's plan, $C_2$, is $C_2 = 44.99 + 0.40a$.

Step2: Set the two cost - equations equal to each other

$39.99+0.45a=44.99 + 0.40a$.

Step3: Solve for $a$

Subtract $0.40a$ from both sides: $39.99+0.45a - 0.40a=44.99+0.40a - 0.40a$, which simplifies to $39.99 + 0.05a=44.99$. Then subtract $39.99$ from both sides: $39.99-39.99 + 0.05a=44.99 - 39.99$, getting $0.05a=5$. Divide both sides by $0.05$: $a=\frac{5}{0.05}=100$.

Answer:

100
It will take 100 additional minutes for the two plans to cost the same.