# Write Two-Variable Linear Inequality Word Problem Worksheet

## 6 problems

Writing a two-variable linear inequality word problem involves crafting a scenario where the relationship between two variables is described using an inequality. These problems typically depict situations where quantities are constrained by conditions such as greater than, less than, greater than or equal to, or less than or equal to specific values. The goal is to describe a real-world context where the solution includes all pairs of values satisfying the inequality.

Algebra 2
Inequalities

## How Will This Worksheet on "Write Two-Variable Linear Inequality Word Problems" Benefit Your Student's Learning?

• Connect math concepts to practical scenarios.
• Develop critical thinking through problem-solving.
• Enhance understanding of graphing inequalities.
• Reinforce skills in manipulating algebraic inequalities.
• Promote logical reasoning in interpreting relationships.
• Enhance comprehension of modeling constraints.
• Prepare for assessments with inequality-based problems.
• Foster self-directed learning and problem-solving confidence.

## How to Write Two-Variable Linear Inequality Word Problems?

1. Decide on two variables to represent quantities related to the problem. For example, let x and y represent quantities like number of items sold, time spent, distances traveled, etc.

2. Determine the relationship between the variables using inequality symbols (<, >, ≤, or ≥), describing conditions like one quantity being less than or greater than another.

3. Create a scenario or context for the problem that involves the variables and their relationship. This could be a business scenario, a travel scenario, a production scenario, etc.

4. Construct a clear and concise word problem that includes:

• A description of the scenario.
• The inequality representing the relationship between the variables.
• Any relevant constraints or conditions.

5. Make sure the problem statement clearly communicates the relationships and constraints, and provides enough information for students to interpret and solve the inequality.

## Solved Example

Q. The manager of an electronics store projects that the store should achieve more than $\8,500$ in revenue from TVs and DVD players every day in order to remain profitable. Its DVD players sell for $\210$, and TVs sell for $\160$.$\newline$Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.$\newline$$x =$ the number of DVD players sold$\newline$$y =$ the number of TVs sold$\newline$$\newline$Choices:$\newline$(A) $160x + 210y < 8,500$$\newline$(B) $210x + 160y < 8,500$$\newline$(C) $160x + 210y > 8,500$$\newline$(D) $210x + 160y > 8,500$
Solution:
1. DVD Player Revenue Calculation: We know:
Price of each DVD player: $\210$
Number of DVD players sold: $x$
What is the total revenue from DVD players?
Price of each DVD player $\times$ Number of DVD players
= $210 \times x$
= $210x$
Total revenue from DVD players: $210x$
2. TV Revenue Calculation: We know:
Price of each TV: $\160$
Number of TVs sold: $y$
What is the total revenue from TVs?
Price of each TV × Number of TVs
= $160 \times y$
= $160y$
Total revenue from TVs: $160y$
3. Total Revenue Calculation: We know: Revenue from DVD players: $210x$ Revenue from TVs: $160y$ What is the total revenue from DVD players and TVs? Add total revenue from DVD players and TVs. $= 210x + 160y$
4. Revenue Requirement Inequality: We know: Total revenue: $210x + 160y$$\newline$ Store's revenue requirement: More than $\8,500$$\newline$ Select the inequality that describes total revenue must be greater than $8,500$.$\newline$ Inequality: $210x + 160y > 8,500$

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