SAT Math word problems

01Read the last line first

The final sentence names the quantity you are solving for. Read it before the story, because it tells you what to write down and what to ignore. A question about two people painting a fence can be asking for a combined rate, a time, or a share of the work, and the algebra is different in each case. Students who read top to bottom discover the question only after building the wrong equation.

02Name the variable with its unit

Write the definition before the equation: let h be the number of hours, let c be the cost in dollars. The unit is not decoration. It tells you whether a rate should be multiplied or divided, and it catches the mistake where a question gives minutes and the answer wants hours. A variable without a unit is a variable you will misuse.

03Translate one clause at a time

Word problems are chains of small statements. Turn each into a piece of algebra as you read, and keep a running list. Of is multiplication, per is division, more than is addition, less than reverses the order, and twice as many is two times. When a clause has no mathematical content, such as a name or a location, it is there for realism and can be crossed out.

04The five shapes that cover most of them

Almost every word problem in the section is one of these, wearing different nouns.

• Fixed cost plus a rate: total equals the fee plus the rate times the quantity
• Two quantities and two facts: a system, one equation for the count and one for the value
• Rate, time and distance: distance equals rate times time, with units converted first
• Mixture or weighted average: the total of one ingredient equals the total of the mix
• Percent change in context: multiply by the multiplier rather than adding a percentage

05The traps that live in the wording

Three phrases decide more marks than any calculation.

• How many more than asks for a difference, not a total
• At least and at most are inequalities, and the boundary is included
• Remaining, left, and still needs asks for the complement, which is the total minus what you just found

06Check with the units, not just the arithmetic

When you have a number, ask what it is measured in and whether that matches the question. A speed in miles per hour multiplied by a time in minutes does not give miles without converting first. A cost in dollars divided by a number of people gives dollars per person, which is not the total. The unit check catches errors that re-reading your own work does not, because it tests the meaning rather than the steps.

07Practice on paper once

Word problems are where speed is least useful. Sit a set on paper, untimed, and write the variable definition for every question even when you can see the answer. The habit is what transfers; the answers are not.

08Questions

Why do I understand the solution but miss the question?

Because the solution is about the algebra and the miss is about the translation. Read the final sentence first and write the variable with its unit before starting; that is usually the whole difference.

How do I deal with too much information?

Cross out anything that is not a quantity or a relationship. Names, places and background details carry no algebra. If a number is given and never used, check whether the question is testing whether you notice.

Should I use a calculator for word problems?

For the arithmetic only, and only once the equation is built. The calculator cannot help you decide what the equation is, and reaching for it early tends to replace thinking with typing.

How do I get faster at these?

Practise the first thirty seconds, not the whole question. Read the last line, define the variable, and say out loud what the equation should represent. Speed comes from that routine becoming automatic.

09Related guides

• Solving systems of equations3 min
• Percent change with multipliers3 min
• The eighteen traps5 min