Question

Cell phone Plan A costs $70 per month and comes with a free phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you choose this Plan B, you will need to purchase a phone for $500. After how many months will the cost of Plan A and the cost of Plan B be the same?

a) 7 months
b) 8 months
c) 9 months
d) 10 months

Answer 1

The cost of Plan A and Plan B will be the same after 25 months, which is not an option listed in the multiple-choice answers provided. A miscalculation must have been made, since the calculation estimating the costs of the plans is to identify the point at which they equate.

Step-by-step explanation:

To determine after which month the costs of Plan A and Plan B are the same, you must set up an equation where the total cost of each plan is equal. The cost of Plan A is $70 each month, so after x months, the cost is 70x dollars. The cost of Plan B is $50 each month plus the initial $500 for the phone, so after x months, the cost is 50x + 500 dollars.

The question is asking when these two costs will be the same, which is when 70x = 50x + 500. To find the value of x, solve this equation:

70x = 50x + 500
x = 500 / 20
x = 25

However, since this answer is not one of the choices given, we need to find the error. By revisiting the algebra, we get the correct calculation:

70x = 50x + 500
20x = 500
x = 500 / 20
x = 25

Since the correct answer is not listed among the provided choices, we should recheck our calculations and make sure to provide the correct methodology to reach the right answer.