Word problems often feel like puzzles wrapped in layers of words, but they’re one of the most powerful ways to understand algebra. They allow students to apply algebraic equations to real-life scenarios, making abstract math concepts come alive. Whether they are calculating how many apples they can buy with a certain budget or figuring out the speed of two trains heading toward each other, word problems help them think logically and organize information.
Here’s a simple approach to suggest students while tackling word problems involving algebraic equations:
1. Understand the Problem
- Read the problem carefully, more than once if needed.
- Identify what the problem is asking you to find. This is usually the unknown, which will become your variable (like x).
2. Set Up an Equation
- Translate words into math.
- Assign variables to unknown quantities and use relationships described in the problem to form an equation.
3. Solve the Equation-Use algebraic methods like:
- Combining like terms
- Isolating the variable
- Balancing both sides of the equation to solve for your unknown.
Equations And Inequalities – Balance The Scales
4. Check Your Answer
- Always plug your solution back into the original problem to see if it makes sense in context. Does your answer seem reasonable? This step ensures you didn’t make an error along the way.
Example: Book Prices Problem
Example problem: “The price of a large book is 5/3 times the price of a small book. If the total cost of 5 small books and 3 large books is $120, what is the price of each?”
Steps:
- Let the price of the small book be x.
- The price of a large book is 5/3 (x)
- The total cost is the sum of 5 small books and 3 large books: 5x+3×5/3 (x)=120
- Simplifying gives: 5x+5x=120 or 10x=120 x=120/10=12
Thus, the small book costs $12, and the large book costs 5/3×12=20
Starting with one-step, one-variable equation word problems will help the students understand how to assign variables to unknown quantities and use relationships described in the problem to form correct equations. With practice, they will start to see patterns and develop strategies for solving more complicated problems.
Below you will find a collection of word problems that can be solved using algebraic equations. The first level is a collection of word problems that can be solved with a one-step, one-variable equation, the second level includes word problems that can be solved with a two-step, one-variable equations, and the third level contains problems that can be solved with 2 or more steps and two variables equations. Every level comes with challenge problems and the solutions are included at the end of the presentation.
