Use the following information. You can work a total of no...

Name: Problem 37, Chapter 7: Algebra 1: Concepts and Skills
Uploaded: 2020-05-16T15:48:36-08:00
Duration: 1 min 6 s
Channel: Aatish Gupta
Description: Use the following information. You can work a total of no more than 20 hours per week at your two jobs. Baby-sitting pays 5 dollars per hour, and your job as a cashier pays 6 dollars per hour. You need to earn at least 90 dollars per week to cover your expenses. Write a system of inequalities that shows the various numbers of hours you can work at each job.

Use the following information. You can work a total of no more than 20 hours per week at your two jobs. Baby-sitting pays 5 dollars per hour, and your job as a cashier pays 6 dollars per hour. You need to earn at least 90 dollars per week to cover your expenses. Write a system of inequalities that shows the various numbers of hours you can work at each job.

Key Concepts

Decision Variables

Decision variables are symbols used to represent the unknown quantities that you need to determine in a problem. In linear programming and systems of inequalities, these typically denote the amounts of resources used, such as the number of hours worked at different jobs, which can be adjusted within the constraints of the problem.

Inequality Constraints

Inequality constraints are conditions expressed using inequality signs, such as '?' or '?', to limit the values of the decision variables. These constraints capture real-world limitations like maximum available time or minimum required earnings, ensuring that any solutions provided must fall within these stipulated boundaries.

System of Inequalities

A system of inequalities is a collection of multiple inequality constraints that must be satisfied simultaneously. This system is used to model situations where several restrictions apply at once, and the solution set represents all possible combinations of decision variable values that adhere to every constraint in the problem.

Linear Relationships

In the context of these problems, linear relationships involve expressions where the decision variables are multiplied by constant coefficients—such as wage rates—to form equations or inequalities. This reflects scenarios where changes in the variables lead to proportional changes in outcomes, such as earnings based on hours worked.

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