Example: Solving a Vacation Trip Budget Application with a Linear Inequality
To determine the amount of work required to fund a vacation trip within a budget, apply the seven-step inequality problem-solving strategy. For example, consider Malik, who plans a vacation costing $ for airfare, $ for food and sightseeing, and $ per night for a -night hotel stay. He has $ in savings and earns $ per hour tutoring.
- Read the problem.
- Identify what to find: the number of hours Malik must tutor.
- Name the unknown: Let = the number of hours.
- Translate into an inequality. The total expenses must be less than or equal to his available funds (savings plus tutoring income):
- Solve the inequality by simplifying and isolating the variable: Which translates to:
- Check: Substituting hours gives . Added to his $ savings, he has $. The expenses exactly equal $, so the answer makes sense.
- Answer: Malik must tutor at least hours to have enough money to pay for the trip.
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Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
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Standardized Strategy for Inequality Applications
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Example: Translating and Solving a Budget Limit Inequality for Purchasing Items
Example: Translating and Solving a Budget Limit Inequality for an Event
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Example: Solving a Vacation Trip Budget Application with a Linear Inequality
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Example: Solving a Road Trip Budget Application with a Linear Inequality
Strategy for Solving Applications with Compound Inequalities
Learn After
Malik is planning a vacation trip with total expenses of 1,875. He has 840 in savings and earns 45 per hour tutoring. He models his situation with the inequality , where is the number of hours he works. Match each description of Malik's budget with its corresponding part of the inequality.
In the example of Malik's vacation budget, the final solution to the linear inequality is , where represents the number of hours he tutors. Based on this result, what is the correct conclusion regarding Malik's work requirement?
The Verification Step in Malik's Budget Plan
Malik is following a systematic seven-step strategy to calculate the number of tutoring hours he needs for his vacation budget. Arrange the following steps in the correct order he should perform them to reach the solution.
When setting up a linear inequality to determine if you can afford a planned expense, such as Malik's vacation trip, your total expenses must be modeled as being greater than or equal to your available funds.