Most SAT Heart-of-Algebra questions are word problems in disguise. The math itself is easy — translating the English into the correct equation is the hard part. The SAT designs its distractors around predictable translation mistakes: reading "5 less than x" as 5 − x instead of x − 5, confusing slope with y-intercept when both are numbers in the sentence, or forgetting to match units (hours vs minutes, dollars vs cents).
The highest-leverage habit is this: before you write any equation, define your variable in writing ("let m = minutes used") and then replace math-trigger words one by one. "Per" → divide or rate. "Of" → multiply. "Is" → equals. "More than" → plus. "Less than" → minus (with the order reversed).
Strategy tip: after solving, plug your answer back into the WORDS of the problem, not just the equation. If the answer doesn't match the story, your equation was wrong — and catching it at this step is much faster than finding the algebra error.
Concept Refresher
SAT word-problem translation in 30 seconds: circle every math-trigger word as you read the problem, then replace them with their symbols. Here's the small vocabulary that covers 90% of SAT translations:
• "is / was / will be / equals" → =
• "of" → × (multiply)
• "per / for each / for every" → rate or ÷
• "more than / increased by / added to" → +
• "less than / decreased by / reduced by" → − (REVERSED order: 'x less than 10' is 10 − x, not x − 10)
• "twice / double" → × 2
• "half / split evenly" → ÷ 2
• "total / combined / sum" → + (add the pieces)
• "times as many / as much" → × (multiply)
Define your variable in writing BEFORE you build the equation. Then write each quantity in the problem in terms of that variable. The equation falls out from the final constraint sentence ("the total was $43", "the sum is 96", etc.).
20 SAT-styled questions. Pick an answer to see the explanation immediately.
1.A gym charges a $50 sign-up fee plus $30 per month. Which equation gives the total cost C after m months?
2.Three less than twice a number is 11. What is the number?
3.A store sells apples for
each and oranges for $3 each. Priya bought 10 pieces of fruit for
3 total. How many oranges?
4.A shirt is on sale for 25% off, and the sale price is $36. What was the original price?
5.The sum of three consecutive even integers is 78. What is the largest of the three?
6.Carlos is 4 years older than twice his sister's age. If Carlos is 22, how old is his sister?
7.A box contains nickels and dimes worth
.75 total. There are 35 coins in all. How many nickels are there?
8.A plumber charges a $60 service call fee plus $85 per hour. If the total bill was $315, how many hours did the plumber work?
9.The length of a rectangle is 3 more than twice its width. The perimeter is 42. What is the width?
10.A train travels 180 miles in h hours. Which expression represents its average speed in miles per hour?
11.Maya is 6 years younger than Lena. In 4 years, Lena will be twice as old as Maya. How old is Maya now?
12.A company sells T-shirts for
5 each. If fixed costs are
00 and variable cost per shirt is $8, how many shirts must they sell to break even?
13.A number plus 7 is equal to 3 times the number minus 5. What is the number?
14.A cellphone plan charges $40 per month plus $0.20 for each text message over 500. If Ava's bill was $52 one month, how many texts over 500 did she send?
15.Tara has
50 and spends
2 per week. Which inequality shows the number of weeks w until she has less than $50?
16.A car rental costs $45 per day plus $0.30 per mile driven. Which expression gives the total cost for d days and m miles?
17.The sum of two consecutive integers is 45. What are the two integers?
18.Jordan invests
,000 at 4% simple interest per year. How much total money will Jordan have after 3 years?
,040
,120
19.A fruit stand sells apples for
.50 each and pears for
each. If Diego spent exactly
7 on a mix of 10 fruits, how many apples did he buy?
20.A tank is filling at a rate of 8 liters per minute. If the tank started with 12 liters, which equation gives the volume V after t minutes?
Frequently Asked Questions
How do I avoid translating the problem backwards?
Circle the 'math trigger' words as you read. Then write each quantity in terms of your variable before you form the equation.
Should I always define a variable for what the question asks?
Usually yes — it makes the final step trivial. But sometimes defining a simpler quantity makes the algebra cleaner, then you compute the asked-for value at the end.
What is the fastest sanity check on a word problem answer?
Plug your answer back into the WORDS of the problem. If the numbers don't match the story, your equation was wrong.