Equations Word Problems

In this lesson, we will learn how to translate word problems into equations and solve them.

Understanding Word Problems

Word problems can often be broken down into simpler parts. The key is to identify what the problem is asking and define the variables involved.

Steps to Solve Word Problems

1. Read the problem carefully: Understand what is being asked.
2. Identify the variables: Assign letters to unknown quantities.
3. Translate the words into an equation: Use mathematical symbols to represent the relationships described in the problem.
4. Solve the equation: Isolate the variable to find its value.
5. Check your solution: Substitute back into the original problem to ensure it makes sense.

Example Problem

Problem: A number increased by 7 is equal to 15. What is the number?

Step 1: Identify the variable. Let the number be represented as $x$.

Step 2: Translate the problem into an equation. The phrase "A number increased by 7" translates to $x + 7$. So, we have:

$$x + 7 = 15$$

Step 3: Solve the equation.

• Subtract 7 from both sides:

$$x = 15 - 7$$

• Simplifying gives:

$$x = 8$$

Step 4: Check the solution. If $x = 8$, then $8 + 7 = 15$, which is correct.

Key Questions

• What are the key phrases in the word problem that indicate mathematical operations?
• How do we define our variables clearly?
• What steps do we follow to ensure we translate the word problem correctly?

Keywords

• Variables
• Translate
• Equation
• Solve
• Check