SAT Math
SAT word problems: turn the wording into an equation
Translate SAT word problems into labeled equations, with examples for rates, percentages, mixtures, quadratics, and the requested quantity.
Define the unknown with its unit, translate the stated relationships, solve, then answer the exact quantity requested. A correct equation matters more than a long list of keyword shortcuts.
Give the variable a job
Suppose a bike rental costs 12 dollars upfront plus 8 dollars per hour. Define as the number of rental hours and as total cost in dollars. Then .
The definition prevents two errors: multiplying the starting fee by the hours and treating the hourly rate as the total. If a customer pays 44 dollars, solve , so hours.
Read the final sentence early. If the question asks for the cost of a six-hour rental, you need , not . Write "find C at h = 6" in words on your scratch paper and calculate dollars.
Translate comparisons in the stated direction
"A has 5 more than twice B" becomes . "A is 5 less than twice B" becomes . "A is twice the sum of B and 5" becomes . Parentheses are part of the meaning.
A club sold adult tickets at 12 dollars and student tickets at 7 dollars. It sold 40 tickets for 380 dollars. With a adults and s students, the equations are and .
Substitute : , giving and . Then . Check both the ticket count and revenue. Meeting only one equation is not enough.
Track units through rates
A tank contains 30 liters and loses water at 2 liters per minute. After t minutes, its volume is , while that constant-rate model remains valid. The tank empties at minutes.
The slope has units of liters per minute. The starting value has units of liters. If the problem asks how many seconds it takes to empty, convert seconds after solving.
For distance, . At 45 miles per hour, a 30-minute trip covers miles. Using 30 directly would mix minutes with an hourly rate. Convert the time or convert the rate, then make the units match.
Percent and mixture equations need a base
A store increases an item's price by 25%, producing a price of 75 dollars. The original p satisfies , so it was 60 dollars. The new amount is the result of a multiplier, not the base for the increase.
For a mixture, suppose 4 liters of 20% salt solution are combined with x liters of 50% salt solution to make a 30% mixture. The salt amount before and after must agree: .
Solving gives , so liters. The final mixture contains liters of salt in 6 liters of solution, and . Adding the percentages would ignore how much of each solution you used.
A geometry story can become a quadratic
A rectangle has area 48 square units. Its length is 2 units greater than its width. With width w, the length is , so .
Rearrange to and factor: . The candidates are and 6, but a width cannot be negative. The dimensions are 6 and 8.
If the question asks for perimeter, you aren't finished at 6. Calculate units. This is why I like writing the requested quantity next to the variable definition: it stays visible after the algebra gets busy.
Use a short check that matches the story
A count of people should be a nonnegative integer. A probability must lie between zero and one. A discounted price should be below the original. These checks don't prove the answer, but they tell you when to reread the setup.
Substitute into the actual relationship, including the units. Then inspect the final question again: dollars, hours, area, or an expression such as ? Select or enter that value.
In the question bank, practice one model type until you can set up its equation without seeing a solution. Then use mixed questions to test whether you can choose the model yourself. Review the first line where your work differs from the problem's meaning; doing more arithmetic won't repair that line.
Try it yourself
Choose an answer.
Luke Finigan is a student developer and the creator of 1600.now, a free Digital SAT practice platform. About Luke.