Solving a Word Problem Using a One-Step Linear Inequality

We have word problems based on real-world situations that can be modeled using one-step inequalities. The solutions of these problems usually have multiple answers over a range of values for which those inequalities are true.

Let us consider the following word problem examples and try to understand how to solve them and obtain the range of values for which these are true.

A contractor is purchasing some tiles for a new patio. Each tile costs $4 and he wants to spend less than $1200. Find the number of tiles he can buy with this amount.

Solution

Step 1:

Let the number of tiles he want to buy be x

Step 2:

Cost of each tile = $4

Cost of x tiles = 4 × x = 4x

Step 3:

Amount he can spend is ≤ $1200

So cost of tiles has to be less than or equal to $1200

4x ≤ 1200

Step 4:

Dividing both sides by 4

4x/4 ≤ 1200/4; x ≤ 300

So the solution of this inequality is

x ≤ 300; The contractor can buy a maximum of 300 tiles.

In 5 years, Sarah will be old enough to vote in an election. The minimum age for voting is at least 18 years. What can you say about how old she is now?

Solution

Step 1:

Let the age of Sarah be x

Step 2:

In 5 years, Sarah’s age = x + 5 which is at least 18 years

x + 5 ≥ 18

Step 3:

Subtracting 5 from both sides

x + 5 −5 ≥ 18 – 5; x ≥ 13

Step 4:

So she is at least 13 years or x ≥ 13