The calculation in a linear word problem may be short. The harder part is deciding what each number means. A starting fee is different from a charge for each hour, and the value of x may not be the quantity the question asks you to report.
Work through the story in three stages: define the variable, build the relationship, then interpret the result. The examples here are original StudyForA questions, not official SAT items.
Put linear equations in context
Algebra is one of the SAT Math content areas, alongside Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. This guide covers one skill within that wider content, not the whole section. See College Board's Math content overview.
The current standard Math section has 44 questions across two 35-minute modules. The second module adapts to performance in the first. Use College Board's test structure and official Bluebook practice for the full test experience; a fixed worksheet cannot reproduce adaptive scoring.
Define the variable with units
Original example: a bicycle hire company charges a fixed fee of $12 plus $5 for each hour. A customer pays $42. How many hours did the customer hire the bicycle?
Let h be the number of hours. The hourly charge is 5h dollars, and the fixed fee is paid once. The equation is 12 + 5h = 42.
Subtract 12 to get 5h = 30, then divide by 5: h = 6. Substituting back gives 12 + 5 × 6 = 42, so the answer is six hours.
Writing h = hours may feel unnecessary, but it prevents you from interpreting the solution as dollars or kilometres later.
Distinguish a starting value from a rate
In C = 12 + 5h, 12 is the cost when h = 0 in the mathematical model. The coefficient 5 describes the increase in cost for each additional hour. It is not the total cost of a five-hour hire.
The context also sets limits. A model might charge only for whole hours, or might allow fractions of an hour. Use the wording supplied instead of assuming every real value is an allowed answer.
When two plans are compared
Suppose plan A costs 12 + 5h dollars and plan B costs 6 + 7h dollars. To find when they cost the same, set the expressions equal:
12 + 5h = 6 + 7h.
Subtract 5h and then subtract 6: 6 = 2h, so h = 3. At three hours, both cost $27. Notice that the answer to “How many hours?” is 3, while the answer to “What is the shared cost?” is 27.
Before three hours, plan B is cheaper; after three hours, plan A is cheaper. Check with one value on each side if you are unsure, rather than guessing from the larger fixed fee.
Try a different context
A water tank contains 180 litres. Water leaves at a constant rate of 12 litres per minute, with no water added. After how many minutes does the tank contain 60 litres?
Let t be time in minutes. The remaining volume is 180 − 12t. Solve 180 − 12t = 60: 12t = 120, giving t = 10 minutes. The negative sign in the model represents a decreasing amount; the elapsed time itself is positive.
Check the requested quantity last
Underline the final question after solving. Does it ask for x, a cost, a rate, or a value such as x + 2? Then confirm units and substitute once. A calculator can support arithmetic, but it cannot decide which relationship the words describe.
Practise SAT skills on StudyForA. Use the feedback to choose another skill; practice accuracy is not an official SAT score prediction.