Multi-Step Equation Word Problems

Multi-step equation word problems require you to translate a real-world scenario into an algebraic equation and then solve it. The main challenge isn't just the math—it's reading the problem, figuring out what you don't know, and writing the correct equation.

Steps to Solve Word Problems

1. Identify the Unknown: Read the problem carefully and decide what you are trying to find. Assign a variable (like $x$ or $n$) to represent this unknown value.
2. Translate Words to Math: Look for keywords. "Twice" means multiply by 2, "sum" or "more than" means addition, and "is" usually means equals.
3. Write the Equation: Combine your variable and numbers into a mathematical sentence.
4. Solve the Equation: Use inverse operations to isolate the variable.
5. Check Your Work: Plug your answer back into the original word problem to see if it makes sense.

Example 1: Translating a Direct Sentence

Problem: Twice a number plus 5 equals 17. What is the number?

• Identify the unknown: Let $x$ be "a number".
• Translate: "Twice a number" is $2x$. "Plus 5" is $+ 5$. "Equals 17" is $= 17$.
• Write the equation: $2x + 5 = 17$
• Solve: Subtract 5 from both sides: $2x = 12$ Divide by 2: $x = 6$

The number is 6.

Example 2: Comparing Two Unknowns

Problem: Tom is 3 years older than Sue. Their ages add up to 27. How old is each person?

• Identify the unknowns: We don't know Sue's age or Tom's age. Let Sue's age be $s$. Since Tom is 3 years older, Tom's age is $s + 3$.
• Write the equation: Their ages "add up to 27". $s + (s + 3) = 27$
• Solve: Combine like terms: $2s + 3 = 27$ Subtract 3 from both sides: $2s = 24$ Divide by 2: $s = 12$

Sue is 12 years old. Since Tom is 3 years older ($12 + 3$), Tom is 15 years old.

Check your work: $12 + 15 = 27$. The answer is correct!