Writing Expressions from Word Problems — ACT Math Guide
Writing expressions from word problems ACT questions test your ability to translate everyday language into mathematical symbols and operations. These problems require you to identify key words, variables, and relationships to create algebraic expressions. The Elementary Algebra domain makes up about 10 questions on the ACT math section, and translating word problems into expressions is a fundamental skill you'll need throughout the 60 questions in 60 minutes. With the right approach, you can confidently decode any word problem the ACT throws at you.
What You Need to Know
Identify key words that indicate operations: "sum" (addition), "difference" (subtraction), "product" (multiplication), "quotient" (division)
Recognize phrases that suggest variables: "a number," "some amount," "twice as much as"
Understand order matters in subtraction and division: "5 less than x" means x - 5, not 5 - x
Look for relationships between quantities: "3 more than twice a number" becomes 2x + 3
Consecutive integers follow patterns: n, n+1, n+2 for consecutive integers
"Of" usually means multiplication in word problems
📐 KEY FORMULA: Practice translating common phrases into algebra
⏱️ ACT TIME TIP: Read the problem twice quickly rather than once slowly — you'll catch more details and stay on pace for 1 minute per question
How to Solve Writing Expressions from Word Problems on the ACT
Example Question 1 — Easy/Medium Difficulty
The sum of three consecutive even integers is 78. If the smallest integer is represented by n, which expression represents the sum?
A) n + (n + 1) + (n + 2)
B) n + (n + 2) + (n + 4)
C) 3n + 6
D) Both B and C
E) n + 2n + 3n
Solution:
Step 1: Identify what "consecutive even integers" means — they're 2 apart
Step 2: If the smallest is n, the next two are n + 2 and n + 4
Step 3: Check if 3n + 6 equals n + (n + 2) + (n + 4) by simplifying
✅Answer: D — Both expressions B and C are equivalent: n + (n + 2) + (n + 4) = 3n + 6
Example Question 2 — Hard Difficulty
Maria has twice as many books as Carlos, and Carlos has 5 fewer books than Ana. If Ana has a books, which expression represents the total number of books all three people have?
A) a + (a - 5) + 2(a - 5)
B) a + (a + 5) + 2a
C) 3a - 5
D) 4a - 15
E) 4a - 10
Solution:
Step 1: Ana has a books
Step 2: Carlos has 5 fewer than Ana, so Carlos has a - 5 books
Step 3: Maria has twice as many as Carlos, so Maria has 2(a - 5) = 2a - 10 books
Step 4: Total = a + (a - 5) + (2a - 10) = 4a - 15
✅Answer: D — Adding all three quantities gives 4a - 15 books total
Common ACT Math Mistakes to Avoid
❌Mistake: Confusing "5 less than x" with "5 minus x"
✅Fix: "5 less than x" means x - 5, while "5 minus x" means 5 - x
❌Mistake: Forgetting that consecutive even integers are 2 apart, not 1
✅Fix: Consecutive integers: n, n+1, n+2; consecutive even: n, n+2, n+4
❌Mistake: Misreading "twice as much as" versus "twice more than"
✅Fix: "Twice as much as x" means 2x; "twice more than x" means x + 2x = 3x
❌Mistake: Not checking if multiple answer choices could be equivalent
✅Fix: Always simplify your expression and compare with all five options A through E
Practice Question — Try It Yourself
A restaurant charges $12 for each pizza plus a $3 delivery fee. If someone orders p pizzas, which expression represents the total cost in dollars?
A) 12p
B) 15p
C) 12p + 3
D) 12 + 3p
E) 12(p + 3)
Show Answer
Answer: C — The cost is $12 per pizza (12p) plus a one-time $3 delivery fee, giving 12p + 3
Key Takeaways for the ACT
Always define your variable clearly before writing the expression
Pay attention to word order — "5 less than x" and "x less than 5" mean different things
Look for keywords that indicate operations, but remember context matters
ACT math writing expressions questions often have multiple equivalent forms as answer choices
Practice identifying consecutive integer patterns since they appear frequently on the ACT test
Related ACT Math Topics
Strengthen your ACT math prep with these related topics:
Solving linear equations →
Substitution and evaluation →