Solve equations of the form f(x)=g(x) approximately by finding graph/table intersections.
Solve a break-even problem by setting models equal
Problem
Plan A costs \(20~\text{dollars}\) plus \(5~\text{dollars}~\text{per}~\text{month}\). Plan B costs \(8~\text{dollars}\) plus \(8~\text{dollars}~\text{per}~\text{month}\). After how many months do the plans cost the same, and what is that cost?
Big Picture
What this problem is really about
Break-even means the two complete cost models have equal outputs for the same month. We’ll build each model from its fixed charge and monthly rate, set the totals equal, and solve for the common input. Then we’ll substitute that month into both models to recover and verify the shared cost, since the full break-even result needs both coordinates with their units.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
