Linear Equations Word Problems

Introduction

Word problems involving linear equations are common in real-life situations. They require translating a verbal description into a mathematical equation.

Key Concepts

1. Identifying Variables: Determine what you need to find and assign variables to those unknowns.
2. Setting Up Equations: Use the information given in the problem to create an equation.
3. Solving the Equation: Use algebraic methods to find the value of the variable.
4. Interpreting the Solution: Ensure that the solution answers the question posed in the word problem.

Example Problem

Problem: A movie theater sells adult tickets for $12 and child tickets for$8. If a total of 50 tickets were sold for $500, how many adult and child tickets were sold?

Step 1: Identify Variables

• Let $x$ = number of adult tickets sold
• Let $y$ = number of child tickets sold

Step 2: Set Up Equations

From the problem, we can create the following equations:

1. Total tickets equation:
   $x + y = 50$
2. Total revenue equation:
   $12x + 8y = 500$

Step 3: Solve the Equations

We can solve these equations using substitution or elimination. Here, we use substitution:

1. From the first equation, solve for $y$:
   $y = 50 - x$
2. Substitute $y$ into the second equation: $12x + 8(50 - x) = 500$ $12x + 400 - 8x = 500$ $4x + 400 = 500$ $4x = 100$ $x = 25$
3. Now, substitute $x$ back to find $y$:
   $y = 50 - 25 = 25$

Step 4: Interpret the Solution

Thus, the theater sold 25 adult tickets and 25 child tickets.

Key Questions

• What are the first steps to take when faced with a word problem?
• How do you identify the variables in the problem?
• What methods can be used to solve the equations once they are set up?
• How can you check your solution to ensure it is correct?

Conclusion

Word problems can seem challenging, but by breaking them down into smaller steps and translating them into equations, you can solve them effectively.