Algebraic word problems: How to turn words into equations

Algebraic word problems can be a challenging aspect of mathematics for many students. However, with a little practice and some useful techniques, turning words into equations can become much easier. Here are some tips to help you translate word problems into algebraic equations:

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1. Read the problem carefully: The first step in solving any word problem is to read it carefully. Make sure you understand the problem statement and all the information given.
2. Identify what you're solving for: The problem will usually ask you to find a specific variable or set of variables. Make a note of what you're solving for, and keep this in mind as you read the problem.
3. Assign variables: Identify the unknown values in the problem and assign them variables. Choose a letter to represent each variable, and make sure to use the same letter throughout the problem.
4. Translate words into symbols: Look for words and phrases that indicate mathematical operations such as "addition," "subtraction," "multiplication," and "division." Translate these words into symbols such as "+," "-", "*", and "/."
5. Write equations: Using the variables and symbols you've identified, write an equation or set of equations that represents the problem. Make sure the equation is balanced and represents the relationship between the variables.
6. Check your answer: Once you've solved the equation, check your answer by plugging it back into the original problem statement. This will ensure that your solution makes sense in the context of the problem.

Here's an example to illustrate these steps:

Problem: Emily has 12 more apples than James. Together, they have 32 apples. How many apples does James have?

Step 1: Read the problem carefully.

Step 2: Identify what you're solving for. In this case, we're solving for the number of apples James has.

Step 3: Assign variables. Let J be the number of apples James has.

Step 4: Translate words into symbols. "Emily has 12 more apples than James" can be translated into E = J + 12. "Together, they have 32 apples" can be translated into E + J = 32.

Step 5: Write equations. Substitute E = J + 12 into the second equation to get (J + 12) + J = 32. Simplify to get 2J + 12 = 32. Solve for J by subtracting 12 from both sides to get J = 10.

Step 6: Check your answer. Plug J = 10 into the original problem statement to see if it makes sense. Emily has 22 apples (12 more than James), and together they have 32 apples, which is consistent with the problem statement.

By following these steps and practicing with different types of word problems, you can develop the skills you need to turn words into algebraic equations. Remember to read the problem carefully, assign variables, translate words into symbols, write equations, and check your answer. With practice and perseverance, you'll become a confident and capable problem solver.