I need to compare the total cost of Plan A and Plan B for different numbers of minutes. Let x be the number of minutes Bob uses the phone. Then the total cost of Plan A is 0.10x, since it is $10$ cents per minute. The total cost of Plan B is 20 + 0.05x, since it has a $\$20$ fee and $5$ cents per minute. I want to find the smallest x such that Plan B is cheaper than Plan A. That means I want to solve the inequality 20 + 0.05x < 0.10x. I can subtract 0.05x from both sides to get 20 < 0.05x. Then I can divide both sides by 0.05 to get 400 < x. This means x has to be greater than 400 for Plan B to be cheaper. But x has to be a whole number, so the smallest possible x is 401. Therefore, Bob has to use the phone for at least 401 minutes to make Plan B the cheaper plan. 
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?