Inequalities Word Problems

Introduction

Inequalities are mathematical expressions that show the relationship between two values, indicating that one is greater than, less than, or not equal to the other. In word problems, we translate real-life situations into inequalities to solve for unknowns.

Example Problem

Problem Statement

A school wants to buy new computers. They have a budget of $3000, and each computer costs $600. How many computers can they buy?

Step 1: Identify the variables

Let $x$ be the number of computers they can buy.

Step 2: Write the inequality

The total cost of the computers must be less than or equal to the budget:

$$600x \leq 3000$$

Step 3: Solve the inequality

To find $x$, divide both sides by 600:

$$\frac{600x}{600} \leq \frac{3000}{600}$$

This simplifies to:

$$x \leq 5$$

This means the school can buy a maximum of 5 computers.

Key Questions

• What is an inequality?
• How can we translate a word problem into an inequality?
• How do we solve an inequality?
• What do the solutions of inequalities represent in real-life scenarios?

Conclusion

Inequalities allow us to express limits and constraints in word problems. By identifying variables and translating scenarios into mathematical expressions, we can find solutions that apply to real-life situations.