Example: Solving a Utility Bill Problem with a Linear Inequality
To determine the maximum usage allowed to keep a utility bill under a specific limit, formulate and solve a linear inequality. For example, if a heating bill has a fixed monthly charge of $5.42 plus $1.08 per therm, and the maximum bill is $87.50, let be the number of therms used. The inequality is . Subtracting gives . Dividing by yields . Thus, a maximum of 76 therms can be used.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
A project coordinator is calculating how many additional contractors can be hired for a seasonal project without exceeding the remaining grant funding. To solve this, they follow a standard seven-step problem-solving strategy. Arrange these steps in the correct sequence from first to last.
In a corporate setting, a manager uses a seven-step strategy to calculate the maximum number of employees that can attend a conference within a fixed travel budget. Which step of this process requires the manager to convert the budget's verbal constraints into a mathematical inequality?
An HR manager is using a seven-step strategy to determine the maximum number of new workstations that can be purchased within a department's quarterly budget. Match each of the following steps of the problem-solving strategy with its corresponding action.
Purpose of the Check Step
A project coordinator is using the seven-step strategy to determine the maximum number of laptops they can purchase for a new department while staying within a fixed budget. True or False: In the 'Solve' step of this strategy, the coordinator should use the Properties of Equality.
A prospective tenant is using a seven-step strategy to determine if their monthly income qualifies for a specific apartment rental. After solving the inequality and checking the result, the tenant must perform the final step of the strategy by stating the conclusion as a(n) ____.
Standardized Strategy for Inequality Applications
Professional Development Budgeting
A warehouse supervisor is using the seven-step strategy to determine the maximum number of inventory pallets a forklift can safely move in a single trip. According to this strategy, what is the primary goal of the Name step?
A facilities manager is using a seven-step strategy to determine the maximum number of energy-efficient windows that can be installed within a fixed renovation budget. According to this strategy, what is the specific objective of the Identify step?
Example: Translating and Solving a Budget Limit Inequality for Purchasing Items
Example: Translating and Solving a Budget Limit Inequality for an Event
Example: Solving a Monthly Phone Bill Application with a Linear Inequality
Example: Solving a Vacation Rental Application with a Linear Inequality
Example: Solving a Utility Bill Problem with a Linear Inequality
Example: Solving a Vacation Trip Budget Application with a Linear Inequality
Example: Solving a Destination Wedding Budget Application with a Linear Inequality
Example: Solving a Road Trip Budget Application with a Linear Inequality
Strategy for Solving Applications with Compound Inequalities
Learn After
In the context of managing a utility budget, consider the linear inequality . Match each component of the inequality to its corresponding real-world meaning.
A facilities manager is planning a budget to keep the monthly heating bill for a warehouse at or below . They use the linear inequality , where represents the number of therms used. In this context, what does the value represent?
A facilities manager is tasked with keeping the monthly heating bill for a commercial warehouse at or below . They use the linear inequality to model the costs, where represents the number of therms used. Arrange the following steps in the correct order to solve for the maximum allowed usage.
A logistics manager uses the inequality to model monthly heating costs for a warehouse. In this model, the term represents the fixed monthly charge that is paid regardless of the number of therms () used.
Budget Limits in Utility Inequalities