# Solve Linear Equations Word Problems Worksheet

## 6 problems

Solving linear equations word problems involves applying algebraic techniques to real-life scenarios described in words. These problems typically require identifying unknown quantities, setting up equations based on given information, and solving for the variables using algebraic operations such as addition, subtraction, multiplication, and division. The solutions provide quantitative answers to questions about quantities, rates, distances, times, and other measurable aspects of the problem situation.

Algebra 2
Equations

## How Will This Worksheet on "Solve Linear Equations Word Problems" Benefit Your Student's Learning?

• Applies algebra to real-life situations.
• Develops critical thinking through problem-solving.
• Reinforces algebraic skills and techniques.
• Enhances mathematical literacy in practical contexts.
• Promotes logical reasoning and systematic approach.
• Deepens understanding of math application in different scenarios.
• Prepares for tests with word problem components.
• Encourages independent learning and confidence in problem-solving.

## How to Solve Linear Equations Word Problems?

• Understand the scenario and identify the unknown quantity (variable) you need to find.
• Let x (or another variable) represent the unknown quantity.
• Use the information given in the problem to set up an equation. This involves identifying relationships such as rates, distances, times, or quantities.
• Use algebraic techniques to solve for the unknown variable. Perform operations like addition, subtraction, multiplication, and division to isolate the variable on one side of the equation.
• Substitute the solution back into the original problem statement to verify its correctness.

## Solved Example

Q. Ms. Chapman wants to take her scout troop to Neon Nights roller rink. The employee she spoke to ahead of time said the total cost for all $9$ people in the group would be $\81$. This includes an entrance ticket and a $\3$ skate rental fee for each person.$\newline$Which equation can you use to find $t$, the cost of each entrance ticket?$\newline$Choices:$\newline$(A) $9(t + 3) = 81$$\newline$(B) $3(t + 9) = 81$$\newline$(C) $3t + 9 = 81$$\newline$(D) $9t + 3 = 81$$\newline$How much does each entrance ticket cost?$\newline$____ $\$
Solution:
1. Identify Cost Components: Identify the total cost and components of the cost for each person. Each person pays for an entrance ticket $t$ and a skate rental fee of $3\$. The total cost for $9$ people is $81\$.
2. Set Up Equation: Set up the equation to represent the total cost.$\newline$The total cost for one person is the ticket price plus the skate rental, so for one person it's $t + 3$ $\$. For $9$ people, it would be $9$ times $(t + 3$ $\$), which gives the equation $9(t + 3) = 81$.
3. Solve for t: Solve the equation for t.$\newline$First, divide both sides of the equation by $9$ to isolate the term with $t$:$\newline$$9(t + 3) = 81$$\newline$$(t + 3) = \frac{81}{9}$$\newline$$t + 3 = 9$$\newline$Next, subtract $3$ from both sides to solve for $t$:$\newline$$t + 3 - 3 = 9 - 3$$\newline$$t = 6$

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