Translate English into y = mx + b: cost, distance, salary, profit, mixtures.
Concept
Almost every linear word problem on the SAT fits the same template: there's a starting value (a fixed amount that exists at x = 0), and a rate (something that changes per unit of the variable).
Cost. Total cost = (rate per item) × (number of items) + (fixed fee).
Drain / decay. Amount left = (starting amount) − (rate of loss) × (time).
The trick is reading units. Words like "per", "each", "every" announce a rate. Words like "to start", "base", "initial", "flat fee", "deposit", "membership" announce a starting value.
Worked example 1 · salary
Sara earns a base salary of $400 per week plus $50 in commission for each item she sells. How many items must she sell in a week to earn $900?
Solution
Setup. Let n = items sold. Pay equation: E = 50n + 400
Equation. Set E = 900: 50n + 400 = 900
Solve.50n = 500 ⇒ n = 10
Sara must sell 10 items. Check: $50(10) + $400 = $900. ✓
Worked example 2 · two-plan comparison
Plan A rents a car for $30 plus $0.20 per mile. Plan B rents the same car for $50 plus $0.10 per mile. At what mileage do the two plans cost the same?
Solution
Setup. Let m = miles. A = 0.20m + 30 · B = 0.10m + 50
Equation. Set the two costs equal: 0.20m + 30 = 0.10m + 50