 Hello and welcome to the session. In this session we will discuss a question which says that you are using between two different cell phones plants. Plan A costs $46.95 per month for 500 minutes plus $0.30 for each additional minute. Plan B costs $14.95 per month for 500 minutes plus $0.40 for each additional minute. How many additional minutes must you use in one month for Plan B to cost more than Plan A? Now let us start with the solution of the given question. Now here we have given two different cell phone plants. Plan A costs $46.95 per month for 500 minutes plus $0.30 for each additional minute. Plan B costs $52.95 per month for 500 minutes plus $0.40 for each additional minute. And we have to find how many additional minutes must be used in one month for Plan B to cost more than Plan A. Thus we have monthly cost for Plan B is greater than monthly cost for Plan A. We have to find number of additional minutes. So let number of additional minutes be m. Now monthly cost of plan equals cost per month for 500 minutes plus times number of additional minutes. Now when number of additional minutes is m then monthly cost of Plan A is equal to $46.95 that is cost per month for 500 minutes plus per minute cost that is $0.30 times number of additional minutes that is m. So monthly cost of Plan A is equal to $46.95 plus $0.30 into m. Similarly monthly cost of Plan B for m additional minutes is equal to $42.95 plus $0.40 into m. Now we have monthly cost for Plan B is greater than monthly cost for Plan A. So using these values we have inequality. Now we have monthly cost of Plan B that is $42.95 plus $0.40 into m is greater than monthly cost of Plan A that is $46.95 plus $0.30 into m or simply we can write as $42.95 plus $0.40 into m is greater than $46.95 plus $0.30 into m. Now let us solve this inequality first and let us subtract $42.95 from both sides of this inequality. So we have $42.95 plus $0.40 into m minus $42.95 is greater than $36.95 plus $0.30 into m minus $32.95. Now further this implies $0.40 into m is greater than $46.95 minus $42.95 is 4 plus $0.30 into m. Now subtracting $0.30 into m from both sides of this inequality we have $0.40 into m minus $0.30 into m is greater than $0.30 into m plus $0.30 into m minus $0.30 into m. Now this implies $0.10 into m is greater than $10. So let us multiply both sides of this inequality by $10. So we have $10 into $0.10 into m is greater than $4 into $10. Now here since we have multiplied by a positive number so inequality does not change. This implies $10 into $10 into m is greater than $40. Further this implies m is greater than $40. This means number of additional minutes is greater than $40. Thus plan B costs more than plan A, more than 40 additional minutes in one month. So this is a solution of the given question. That's all for this session. Hope you all have enjoyed the session.