Question

describe a real-life setting in which a systems of equations approach would be useful. Identify a problem situation or exploration you will engage in which will require you to apply linear functions to real-life setting.

Answer 1

Almost any situation where there is an unknown quantity can be represented by a system of equations , like figuring out income over time, calculating mileage rates, or predicting profit.

Suppose there is a problem situation that is completely related to our real life.

Anne is trying to choose between two phone plans. The first plan, with Vendafone, costs $20 per month, with calls costing an additional 25 cents per minute. The second company, Sellnet, charges $40 per month, but calls cost only 8 cents per minute. Which should she choose?

You should see that Anne's choice will depend upon how many minutes of calls she expects to use each month. We start by writing two equations for the cost in dollars in terms of the minutes used. Since the number of minutes is the independent variable, it will be our x.

Cost is dependent on minutes - the cost per month is the dependent variable and will be assigned y.

For Vendafone: y = 0.25x + 20
For Sellnet: y = 0.08x + 40

So , by plotting a graph we get :

The line for Vendafone has an intercept of 20 and a slope of 0.25. The Sellnet line has an intercept of 40 and a slope of 0.08 (which is roughly a third of the Vendafone line's slope). In order to help Anne decide which to choose, we'll find where the two lines cross, by solving the two equations as a system.

So if Anne uses 117.65 minutes a month (although she can't really do exactly that, because phone plans only count whole numbers of minutes), the phone plans will cost the same. Now we need to look at the graph to see which plan is better if she uses more minutes than that, and which plan is better if she uses fewer. You can see that the Vendafone plan costs more when she uses more minutes, and the Sellnet plan costs more with fewer minutes.

So, if Anne will use 117 minutes or less every month she should choose Vendafone. If she plans on using 118 or more minutes she should choose Sellnet.