Writing an Inequality for a Real-World Situation

Introduction

There are many real-world situations, which we can reduce to inequalities and if needed, we solve them as well.

Example 1

Shawna needs to buy some pencils and an eraser. She can spend no more than $9. The eraser costs $1 and the pencils cost $0.25 each. Let the number of pencils Shawna buys be p. Write an inequality for this situation.

Solution

Step 1:

Given eraser cost = $1; pencil cost = $0.25

Amount paid = 0.25p + 1 ≤ 9

Step 2:

Inequality representing the above real-world situation is 0.25p + 1 ≤ 9

Example 2

More than 370 students went on a field trip. Twelve buses were filled and 10 more students traveled in a car. Let s represent the number of students in each bus. Write an inequality for this situation.

Solution

Step 1:

Number of buses = 12; Students in each bus = s; students in car = 10; Total students = 12s + 10 > 370

Step 2:

Inequality representing the above real-world situation is 12s + 10 > 370