Question

Please help with this math question:

You are choosing between two different cell phone plans. The first plan charges a rate of 21 cents per minute. The second plan charges a monthly fee of $29.95 plus 10 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

To determine how many minutes you would have to use in a month for the second plan to be preferable, we can set up an equation to compare the costs of the two plans.

Let M represent the number of minutes used in a month. The total cost for the first plan is 21 cents per minute, so the cost for the first plan is 0.21M dollars.

The total cost for the second plan consists of the $29.95 monthly fee plus 10 cents per minute, which is 0.10M dollars. Therefore, the cost for the second plan is 29.95 + 0.10M dollars.

Now, we want to find the point at which the cost of the second plan is equal to or less than the cost of the first plan. So, we set up an equation:

29.95 + 0.10M ≤ 0.21M

Now, let's solve for M:

Subtract 0.10M from both sides of the inequality:

29.95 ≤ 0.21M - 0.10M

29.95 ≤ 0.11M

Now, divide both sides by 0.11 to isolate M:

M ≥ 29.95 / 0.11

M ≥ 272.27 (approximately)

So, you would need to use 273 minutes or more in a month for the second plan (with the $29.95 monthly fee) to be preferable over the first plan (charging 21 cents per minute).