How to Solve Any Algebra Word Problem: The 5-Step Translation Method

Most people who struggle with algebra word problems don’t have a math problem — they have a translation problem. A word problem is a story with the numbers hidden inside it, and the skill that matters is converting sentences into an equation you can solve. This guide walks through a repeatable 5-step method, a phrase-to-math cheat sheet, and three worked examples ranging from simple to tricky.

The 5-Step Translation Method

1. Find the question. The last sentence usually tells you what to solve for. Write it down before anything else.
2. Define your variable. Pick the unknown and state it clearly: “let x = the daughter’s current age.” Never skip this step — it forces you to understand the problem.
3. Translate key phrases. Convert words to math using the cheat sheet below.
4. Build the equation. Connect the translated pieces with an equals sign based on the relationship described in the story.
5. Solve, then check. Plug your answer back into the story. If it doesn’t make sense in the real world, re-read the problem.

Phrase-to-Math Cheat Sheet

English Phrase	Math	Example
“is”, “equals”, “results in”	=	“the total is 50” → = 50
“sum of”, “more than”, “increased by”	+	“5 more than x” → x + 5
“less than”, “decreased by”, “difference”	−	“3 less than x” → x − 3 (careful: not 3 − x)
“twice”, “double”, “times”, “product”	×	“twice the price” → 2p
“half of”, “divided by”, “per”	÷	“half of the total” → t ÷ 2
“consecutive integers”	n, n+1, n+2	“three consecutive numbers” → n, n+1, n+2

Worked Example 1: The Classic Age Problem

“A father is three times as old as his son. In 12 years, he will be twice as old as his son. How old is the son now?”

Step 1: We need the son’s current age.
Step 2: Let x = the son’s age now, so the father’s age now is 3x.
Step 3: In 12 years: son = x + 12, father = 3x + 12.
Step 4: “He will be twice as old” → 3x + 12 = 2(x + 12).
Step 5: 3x + 12 = 2x + 24 → x = 12. Check: son 12, father 36; in 12 years son 24, father 48 = 2 × 24. ✅

Worked Example 2: Consecutive Integers

“The sum of three consecutive integers is 72. Find the integers.”

Let the integers be n, n+1, n+2. Then n + (n+1) + (n+2) = 72 → 3n + 3 = 72 → n = 23. The integers are 23, 24, 25. ✅

Worked Example 3: The Mixture Problem

“A coffee shop blends a $12/lb bean with a $7/lb bean to make 20 lb of a $9.50/lb blend. How many pounds of each?”

Let x = pounds of the $12 bean, so 20 − x = pounds of the $7 bean. Value equation: 12x + 7(20 − x) = 9.50 × 20 → 12x + 140 − 7x = 190 → 5x = 50 → x = 10. Use 10 lb of each. ✅

Common Mistakes and How to Avoid Them

• “Less than” reversal: “5 less than x” is x − 5, not 5 − x. Read the phrase as “x, with 5 taken away.”
• Skipping the variable definition: If you can’t say what x stands for out loud, you don’t understand the problem yet.
• Forgetting units: Always write “let x = age in years” — mixing minutes and hours will silently break your answer.
• Not checking the answer: A solved equation that contradicts the story is still wrong.

Once you’ve translated a problem into an equation, the rest is mechanical — and if you’d rather skip the arithmetic, plug it into the Algebra Calculator at Today Calculator to solve and verify your work step by step.