Word Problems in Real-World Applications

In this lesson, we will explore how to solve word problems that apply to real-life situations. Word problems often involve translating words into mathematical equations. Let's break down the steps to solve these problems effectively.

Steps to Solve Word Problems

1. Read the Problem Carefully: Understand what is being asked.
2. Identify Key Information: Look for numbers, units, and specific conditions.
3. Define Variables: Let variables represent unknowns in the problem.
4. Translate into an Equation: Use the information to form an equation.
5. Solve the Equation: Use appropriate methods to find the value of the variable.
6. Check Your Work: Verify that your answer makes sense in the context of the problem.

Example Problem

A store sells apples for $3 each and bananas for $2 each. If you buy a total of 10 fruits and spend $24, how many of each fruit did you buy?

Step 1: Define Variables

• Let $a$ = number of apples
• Let $b$ = number of bananas

Step 2: Set Up Equations

From the problem, we can create two equations:

1. Total fruits: $a + b = 10$
2. Total cost: $3a + 2b = 24$

Step 3: Solve the Equations

From the first equation, we can express $b$ in terms of $a$: $b = 10 - a$

Now, substitute $b$ into the second equation: $3a + 2(10 - a) = 24$

Simplifying gives: $3a + 20 - 2a = 24$
$a + 20 = 24$
$a = 4$

Now substitute $a$ back to find $b$: $b = 10 - 4 = 6$

Step 4: Conclusion

You bought 4 apples and 6 bananas.

Key Questions

• What steps do you take to identify the relevant information in a word problem?
• How do you decide what variables to use in your equations?
• Why is it important to check your work after solving a problem?

Keywords

• Word Problems
• Variables
• Equations
• Real-World Applications
• Problem Solving