jmc

Question

Bob is trying to decide between two cell phone plans. Plan A has no flat fee, but the user must pay 10 cents per minute on the phone. Plan B requires a one-time fee of 20, but only requires a payment of 5$ cents per minute on the phone. What is the minimum whole number of minutes Bob has to use the phone for to make Plan B the cheaper plan?

Accepted Answer

Let x be the number of minutes that Bob anticipates using. Plan A costs 10x cents, while Plan B costs 2000 + 5x cents. We therefore have the inequality align* 2000+5x &< 10x 2000 &< 5x 400 &< x. align* The smallest integer x such that 400 < x is 401. Therefore, Bob must use at least 401 minutes to make Plan B cheaper.