Create and solve a one-variable linear equation from a short context.
Write and solve a break-even equation with the variable on both sides
Problem
Plan A costs \(\$20\) plus \(\$5~\text{per}~\text{month}\). Plan B costs \(\$8\) plus \(\$8~\text{per}~\text{month}\). Write an equation for equal total costs and solve for the month when the plans cost the same.
Big Picture
What this problem is really about
Each plan has a starting cost and a monthly cost, so we need one complete expression for each plan. Break-even occurs when those two totals are equal for the same month, which puts the variable on both sides. We’ll set the expressions equal, collect the monthly terms and fixed costs, and solve for the meeting time.
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