Question

You are choosing between two different cell phone plans. The first plan charges a rate of 22 cents per minute. The second plan charges a monthly fee of $44.95 plus 11 cents per minute.

How many minutes would you have to use in a month in order for the second plan to be preferable?

Answer 1

Answer: it would take 409 minutes before the second plan is preferable.

Explanation:

Let x represent the number of minutes that you used

with either the first plan or second plan

Let y represent the total cost of x minutes with the first plan.

Let z represent the total cost of x minutes with the second plan.

The first plan charges a rate of 22 cents per minute. This means that the total cost of x minutes would be

y = 22x

The second plan charges a monthly fee of $44.95(4495 cents) plus 11 cents per minute. This means that the total cost of x minutes would be

z = 11x + 4495

Let us determine the number of minutes before the cost of x minutes using both plans becomes the same, we would equate y to z. It becomes

22x = 11x + 4495

22x - 11x = 4495

11x = 4495

x = 408.63

Since the second plan is cheaper with more minutes, if we go beyond x, it will be cheaper than the first plan. So wen x is 409,

First plan = 22×409 = 8998 cents

Second plan = 11×409 + 4495 = 8994 cents. Second plan is lower at 409 minutes