a Let's write a system of equations for the described situation. Let x be the number of text messages we send or receive and y be the total cost for the plan. For the first plan we have to pay $ 40 per month plus $ 0.20 for each text message sent or received: 0.20 x. With this information we can write an equation for the cost of this plan.
y= 40+ 0.20 xA comparable plan costs $ 60 per month, regardless of the number of messages we send or receive. Let's write an equation for this.
y= 60
Together these equations form a system of equations.
y= 40+ 0.20 x y= 60
Let's graph the system to find its solution.
We can see that the graphs intersect at the point (100,60). This tells us that we would have to send or receive 100 text messages for the plans to cost the same each month.
b We can decide which plan is better for only sending 50 messages by analyzing the graphs we created in Part A. Since the horizontal line is constantly y=60, we only need to analyze the graph of the first phone plan.
We can see that for the first cell phone plan we will pay $50 per month, which is less than $60. Therefore, it is more logical to buy the first plan.
