Learn Before
Solving a Budget-Constrained Purchase Problem Using a Linear Inequality
Apply the seven-step inequality strategy to a problem that requires rounding a non-integer algebraic result to a whole number.
Problem: Dawn won a $4,000 mini-grant to buy tablet computers for her classroom. Each tablet costs $254.12 (including tax and delivery). What is the maximum number of tablets she can buy?
- Read the problem.
- Identify what to find: the maximum number of tablets Dawn can buy.
- Name the unknown: Let = the number of tablets.
- Translate into an inequality: "$254.12 times the number of tablets is no more than $4,000" becomes
- Solve by dividing both sides by :
Since must be a whole number of tablets, round down to .
- Check: Rounding the price down to $250, 15 tablets would cost $3,750 and 16 tablets would cost $4,000, so a maximum of 15 tablets at $254.12 each is reasonable.
- Answer: Dawn can buy a maximum of 15 tablets.
This example illustrates that when the algebraic solution is not a whole number and the variable represents a count of items, the result must be rounded down because purchasing 16 tablets would exceed the budget.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.3 Math Models - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Related
Addition Property of Inequality
Subtraction Property of Inequality
Multiplication Property of Inequality
Division Property of Inequality
Solution of an Inequality
Strategy for Solving Applications with Linear Inequalities
Solving a Rent Affordability Problem Using a Linear Inequality
Rounding Inequality Solutions to Whole Numbers in Applications
Solving a Budget-Constrained Purchase Problem Using a Linear Inequality
Linear Inequality in Two Variables
A logistics coordinator uses mathematical statements to ensure that shipping weights do not exceed a truck's capacity. When using a 'linear inequality' for this purpose, the variable in the expression must be raised to which power?
In a professional logistics context, a linear inequality (such as 'Weight <= 5000') typically results in only one specific numerical solution.
In a professional business environment, managers use specific mathematical symbols to define operational constraints and targets. Match each inequality symbol with the phrase that correctly describes its application in a workplace scenario.
Warehouse Capacity Planning
Visualizing Operational Thresholds
In a professional workplace, when a supervisor defines a budget limit or a safety threshold using a mathematical statement that connects two algebraic expressions with an inequality symbol and features a variable raised only to the first power, this statement is known as a(n) ________ ________.
Structural Requirements of Inequalities
A software developer is writing the logic for a budgeting tool that uses mathematical constraints to trigger alerts. Arrange the following structural components and characteristics in the correct order to describe the formal definition of a linear inequality.
A procurement officer uses a linear inequality to define the maximum price per unit they are willing to pay for a new contract. In this professional context, which of the following best defines the 'solutions' to that linear inequality?
A business analyst is organizing a training manual for a new budget tracking tool that uses mathematical constraints. Match each component of the tool's logic with its correct mathematical classification.
Example: Solving and Graphing One-Step Linear Inequalities
Solving Multi-Step Linear Inequalities
Collecting Variables on the Side with the Largest Coefficient When Solving Inequalities
Identity Inequality
Contradiction Inequality
Solving and Graphing Compound Inequalities with 'or'
Learning Objectives for Solving Linear Inequalities
Compound Inequality
Graphing the Solution Set of a Linear Inequality on a Number Line
Learn After
When using a linear inequality to determine the maximum number of whole units that can be purchased within a fixed budget, what is the standard rule for rounding a non-integer result like n <= 15.74?
A procurement officer is calculating the maximum number of safety vests that can be ordered for a construction crew without exceeding a $1,200 budget. According to the standard strategy for budget-constrained problems, if the algebraic solution is n <= 45.7, the officer must round the result ____ to the nearest whole number.
A department manager is using the standard problem-solving strategy to determine the maximum number of new ergonomic chairs she can purchase with a fixed equipment budget. Arrange the following steps of the strategy in the correct order.
In a budget-constrained purchase problem, if the algebraic solution to a linear inequality is , the manager can purchase a maximum of 26 whole items while staying within the budget.
In a professional procurement setting, project leads use a standard seven-step strategy to solve budget-constrained purchase problems. Match each step of the strategy below with the specific action taken during that phase.
Rounding Standards in Budget-Constrained Procurement
Corporate Equipment Procurement Strategy
Rounding Rules in Budget-Constrained Procurement
A department manager uses a linear inequality to determine the number of new laptops they can buy without exceeding a fixed equipment budget. If the algebraic solution is , why is the manager required to round the final answer down to 15 laptops?
An office manager is setting up a mathematical statement to ensure that the total cost of a new equipment order does not exceed the department's funding. If the manager is told that the total cost must be 'no more than' the budget amount, which mathematical symbol correctly represents this constraint?