I want detail answer

Question

You are choosing between two different cell phone plans. The first plan charges a rate of 20 cents per minute. The second plan charges a monthly fee of $34.95 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

Let us set up an inequality and solve it.

Let us say that you use m minutes per month.

Were you to chose the first plan, you would pay

P₁ (m) = 0.2 m dollars (because 20 cents = 0.2 dollars)

Were you to chose the second plan you would pay

P₂ (m) = 34.95 + 0.1 m dollars (because 10 cents = 0.1 dollars)

The second plan being preferable means that you would pay less

P₂ (m) < P₁ (m)

34.95 + 0.1 m < 0.2 m

solving for m we get

34.95 < 0.1 m

349.5 < m

Or translating back to English, the second plan is preferable if you use more than 349.5 minutes per month (or on average more than 11.65 minutes per day).

Answer 2