When we work through algebra word problems, we read a situation written in plain language and rewrite it as a mathematical equation.
We often notice 7th and 8th graders stumble at this translation step. That is completely normal. It happens because translating requires students to combine reading skills with algebra knowledge.
With that in mind, Mathnasium tutors put together this guide to explain how to read word problems carefully, translate keywords into operations, and set up equations confidently.
Translating word problems into equations follows a reliable process we can apply to any problem, no matter which operations it calls for. Every algebra problem follows the same translation logic, and these four steps can serve as our guide.
To see how the steps work in practice, let’s walk through a simple example:
“Maya bought a $6 poster and four books. If each book costs the same and she spent $38 in total, how much did each book cost?”
We always read the entire problem carefully to get the context before we write anything down.
If we skip this step, we often miss an important condition buried at the end of the problem or assign a variable to the wrong quantity.
From there, we identify what the problem asks us to find and assign it a variable.
We write a quick note to stay on track. For our problem, we want to find the price of one book, so we write:
Let x equal the cost of one book.
After we set our variable to represent the unknown quantity, we are ready for the next step.
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To choose the right operations, we scan the text for clue words. We can use this reference table as a starter guide, though we still need to pay attention to context:
|
Operation |
Keywords |
|
sum, total, more than, increased by, combined, in all, added to |
|
|
less than, decreased by, difference, fewer than, remaining, subtracted from |
|
|
times, product, of, multiplied by, per, each, every |
|
|
divided by, split equally, quotient, shared among, per |
Notice that "per" appears under both multiplication and division. When we know a rate and need a total, "per" means multiplication. When we split a total into equal parts, "per" means division.
Now back to Maya’s problem:
The phrase "each book costs the same" tells us we need to multiply our variable (x) by 4.
The poster price is a single fixed cost, which tells us we need to add 6.
After we set our variable and choose our operations, we translate the words into an equation sentence by sentence.
For Maya's problem, our equation looks like this:
4x + 6 = 38
We write the complete equation before we do any math. This lets us double-check our setup and spot a misread keyword before we start the arithmetic.
Now we solve for the variable. To isolate x, we undo each operation using its inverse, subtracting what was added, and dividing what was multiplied.
Think of an equation as a balanced scale; whatever we do to one side, we must do to the other.
For Maya’s problem (4x + 6 = 38), we work backward in two steps:
Subtract the fixed cost: Subtract 6 from both sides to get 4x = 32.
Undo the multiplication: Divide both sides by 4 to get x = 8.
Finally, we substitute our answer back into the original equation to verify it balances:
4(8) + 6 = 38 → 32 + 6 = 38
All good!
When we check our work, we catch setup errors that simple arithmetic misses. If the numbers do not balance, we know to revisit our variable setup and keywords.
Let’s go through a few more examples together to make our setup skills rock-solid.
A number increased by 14 equals 31. What is the number?
First, we identify the unknown and write the number we are looking for as x.
Next, let’s scan for keywords; in this case, we see “increased by”, which means we need to add the number to x.
Write down the equation as (x + 14 = 31)
We solve by subtracting 14 from both sides, and we come to the conclusion that x equals 17. To check if we have done the math correctly, we can put 17 into the original problem: 17 + 14 = 31.
Leo and Mia participated in a trivia contest. Mia scored 15 more points than Leo, and their total score was 105 points. How many points did Leo score?
In this case, the unknown is the number of points Leo scored, and we will mark it with x.
We identify “more than” as our keyword, so it’s clear that we need to perform addition.
Write out the equation: (x + (x + 15) = 105)
The unknown x shows up twice, so we can combine the like terms and end up with 2x + 15 = 105
Subtract 15 from both sides to get 2x = 90, then divide both sides by 2. The final answer is: x = 45
To verify the answer, place it back in the original equation: 45 + (45 + 15) = 105.
Jake earns the same amount of money per dog walk. After 3 walks, he uses $8 from his earnings for snacks. He has $19 remaining. How much does Jake earn per walk?
We identify the unknown as the amount of money Jake earns per walk; this is the value that we will write as x.
We can see two keywords here. "Per" signals multiplication since Jake earns x dollars for each of his 3 walks, and "remaining" signals subtraction.
We set up the equation: 3x - 8 = 19.
We add 8 to both sides first, which gives us 3x = 27, then divide both sides by 3 to get the solution: x=9. Double-check the answer, just in case: 3(9) - 8 = 19. All good!
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We have covered the full translation process and worked through some examples together. Now it’s time to try a few problems independently.
Use the steps and the keyword table as your guide.
Problem 1: A bowling alley charges a flat fee of $6 for shoe rental, plus $4 for every game played. If David spends a total of $26, how many games did he play?
Problem 2: A teacher divides a box of pencils equally among 6 lab stations. After placing the pencils at the stations, she had 4 pencils left over. If the box had 52 pencils, how many did she place at each lab station?
Problem 3: A youth baseball league splits its players equally into 5 teams, with 3 extra players assigned as substitutes. If there are 68 players in total, how many are in each team?
Problem 4: A bakery starts the morning with 96 fresh muffins. The baker sells 8 muffins per hour. At the end of his shift, there are 16 muffins left. How many hours did the baker work?
When you finish, check your answers at the bottom of our guide.
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At Mathnasium, our specially trained tutors use a mix of verbal, visual, mental, tactile, and written techniques to make math concepts like algebra word problems make sense.
Mathnasium is a math-only learning center dedicated to helping K–12 students of all skill levels succeed in math. Whether a student is trying to fill in foundational knowledge gaps, keep up with their schoolwork, or get ahead in their math journey, we are here to help.
Our proprietary teaching approach, the Mathnasium Method™, is designed to follow each student's learning style and goals to help them truly understand math.
Our approach includes:
Assessment and Personalized Learning Plans: Every student starts with a diagnostic assessment. Here, we discover their relationship with math, their skills, and knowledge gaps. We use this to build a personalized learning plan that matches both their current achievements and future goals. Whether they need help with foundational math topics or something specific like algebra word problems, we have a plan and solution!
Teaching for Understanding: Our tutors use natural language and a mix of verbal, visual, mental, tactile, and written techniques to make each concept easy to understand.
Problem-Solving and Critical Thinking: Even though we are always there to help, during sessions we encourage students to try to solve problems on their own. This helps them develop problem-solving skills that are the basis for further development. If needed, our tutors are always there to offer guidance.
An Engaging and Fun Learning Environment: Our sessions include fun activities, so students actually look forward to learning. To help boost their confidence, we celebrate and award each milestone.
The impact goes beyond classroom success:
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We have over 1,100 learning centers across North America, so there is likely a Mathnasium nearby.
Families in Round Rock East and the neighboring areas can access that same approach at Mathnasium of Round Rock East.
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Take a look at the solutions and see if you’ve solved the problems correctly.
Problem 1: 4x + 6 = 26 → x = 5
Problem 2: 6x + 4 = 52 → x = 8
Problem 3: 5x + 3 = 68 → p = 13
Problem 4: 96 - 8x = 16 → x = 10
Mathnasium of Round Rock East is a math-only learning center for K-12 students in Round Rock, TX. Trusted by over a million parents, Mathnasium uses personalized learning plans and the proprietary Mathnasium Method™ to help students catch up, keep up, and get ahead on their math journey.
Our specially trained tutors deliver face-to-face instruction in a supportive and fun small-group environment, working with students both in center and online to develop a deep understanding of math, build confidence, and improve academic performance.
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