How to turn a word problem into an equation
A word problem can be difficult even when you know how to solve the equation. The first job is to describe what changes and what stays fixed. Once the quantities have names, you can write a relationship that matches the story and test whether your answer makes sense.
Read for the question and the quantities
Read the whole problem once. Underline what you must find, circle the numbers with their units, and mark words that describe a relationship, such as “each”, “altogether” or “more than”. Do not choose an operation from a single word. Read the sentence around it to see which quantity it describes.
Separate known values from the unknown. If the question asks for the price of one item, let x mean that price and write its unit. If it asks for a number of people, x is a count. A variable with a clear meaning is easier to check than an x written beside a string of numbers.
Write the relationship before calculating
Put the story into one sentence using the quantities you named. For example: “cost of the repeated items plus the fixed charge equals the total.” Then replace each part with a number or expression. If you cannot say what every term represents, return to the story before solving.
A small sketch, table or bar can help when several quantities are compared. Keep the same unit on both sides of an addition or equality. A count of tickets cannot be added directly to a price in currency; the count first needs to be multiplied by the price per ticket.
Work through a complete example
Suppose a fictional school club buys three identical notebooks and pays a fixed delivery charge of 4 units of currency. The total is 25 units. What is the price of one notebook? This is an invented practice problem, not a real purchase or school policy.
Let x be the price of one notebook in units of currency. Three notebooks cost 3x. The delivery charge is added once, so the relationship is 3x + 4 = 25. Subtract 4 from both sides to get 3x = 21, then divide both sides by 3. One notebook costs 7 units.
Check in the original story: three notebooks at 7 units each cost 21 units; adding the 4-unit delivery charge gives 25 units. The answer has the right unit and is smaller than the total. Writing 3(x + 4) = 25 would charge delivery three times, so it describes a different story.
Use a short translation template
For your next problem, write five lines: “Find: [quantity and unit]. Let x = [meaning and unit]. Story relationship: [one sentence]. Equation: [expression = expression]. Check: [put the answer back into the story].” The relationship sentence should be understandable before you do any algebra.
If the question compares two unknown amounts, define one variable and express the other in terms of it. For example, if one length is 5 cm longer than another, write “shorter length = x cm” and “longer length = x + 5 cm”. Check which length the question actually asks you to report.
Find the first point where an answer goes wrong
If your answer fails the story check, read the equation term by term. Did you count a fixed charge more than once, reverse “more than” and “less than”, or mix units? If the equation matches the story, check each algebra step separately. This tells you whether the problem is in translation or calculation.
Some stories do not give enough information for one answer, and some answers are impossible in context, such as a negative number of notebooks. Say what is missing or why the result cannot describe the situation. If you are unsure which relationship the problem states, show your variable definitions and your proposed equation to a teacher, along with the sentence you used to build it.
