Application: Rate Plans

Property Create a system of equations where each equation represents a different rate plan. The variables typically stand for cost $(y)$ and a unit of time or quantity $(x)$. The solution $(x, y)$ is the break even point where both plans cost the same. Explanation Is the expensive gym with no sign up fee a better deal than the cheap gym with a big fee? Systems of equations can tell you! By turning each option into an equation and graphing them, the intersection point shows the exact moment their costs are equal. This helps you figure out which plan saves you more money in the long run. Examples Phone Plan A costs 20 dollars per month plus 10 dollars per gigabyte: $y = 10x + 20$. Plan B is 40 dollars per month plus 5 dollars per gigabyte: $y = 5x + 40$. The lines intersect at $(4, 60)$, meaning at 4 gigabytes, both plans cost 60 dollars. Car Rental A is 50 dollars plus 1 dollar per mile: $y = x + 50$. Car Rental B is 2 dollars per mile: $y = 2x$. They intersect at $(50, 100)$. At 50 miles, both rentals cost 100 dollars.