Linear Equations Word Problems

In this lesson, we will explore how to solve word problems involving linear equations. A linear equation is typically in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. When faced with a word problem, the first step is to translate the words into mathematical equations.

Example Problem

Problem: A company sells pencils for $0.50 each and erasers for$0.75 each. If a customer buys a total of 20 items and spends $12.00, how many pencils and erasers did they buy?

Step 1: Define the variables.

• Let $x$ be the number of pencils.
• Let $y$ be the number of erasers.

Step 2: Set up the equations based on the problem.

• From the total items: $x + y = 20$
• From the total cost: $0.50x + 0.75y = 12$

Step 3: Solve the first equation for $y$.

• $y = 20 - x$

Step 4: Substitute $y$ in the second equation.

• $0.50x + 0.75(20 - x) = 12$

Step 5: Distribute and simplify.

• $0.50x + 15 - 0.75x = 12$

Step 6: Combine like terms.

• $-0.25x + 15 = 12$

Step 7: Isolate $x$.

• $-0.25x = 12 - 15$
• $-0.25x = -3$
• $x = 12$

Step 8: Substitute back to find $y$.

• $y = 20 - 12 = 8$

Conclusion: The customer bought 12 pencils and 8 erasers.

Key Questions

• How can you identify the variables in a word problem?
• What steps do you take to set up equations from word problems?
• How do you check your solutions once you have found them?
• What is the significance of the slope and y-intercept in real-world applications?
• Can you give another example of a linear equation word problem?

Keywords

• Linear equations
• Word problems
• Variables
• Equations
• Solutions