Final answer:
The costs of the two cell phone plans will be the same after 5 months, which is the solution to the equation obtained by equating the two total cost expressions.
Step-by-step explanation:
The student's question revolves around finding out after how many months two cell phone plans, one from Verizon with an upfront cost and a monthly fee, and another from T with just a monthly fee, will cost the same. To solve this, we can set up an equation based on the cost information provided. Let m represent the number of months after which the two plans have the same total cost.
Verizon's plan: $125 sign-up fee + $50/mo = $125 + $50m
T's plan: $75/mo = $75m
To find out when the costs are the same, we set the two expressions equal to each other: $125 + $50m = $75m. Solving for m gives us m = 5. Therefore, after 5 months, the costs of the two plans will be the same.