Inequalities and Earnings Analysis

The video tutorial explains how to set up a system of inequalities from a word problem. It involves identifying variables for two jobs, house cleaning and sales, and setting up inequalities based on hours worked and money earned. The tutorial guides through the process of formulating inequalities using given constraints, such as total hours and minimum earnings, and concludes with the complete system of inequalities.

What is the first step in setting up a system of inequalities from a word problem?

• Identify the variables involved

• Calculate the total earnings

• Determine the maximum hours

• Write the final solution

In the given problem, what do the variables x and y represent?

• x is total hours, y is total earnings

• x is house cleaning hours, y is sales job hours

• x is sales job hours, y is house cleaning hours

• x is earnings from sales, y is earnings from cleaning

What is the pay rate for the house cleaning job?

• $8 per hour

• $10 per hour

• $5 per hour

• $7 per hour

How many hours can you work in total at both jobs?

• No more than 41 hours

• At least 41 hours

• Exactly 41 hours

• No more than 50 hours

What inequality symbol is used to represent 'no more than 41 hours'?

• Greater than

• Less than or equal to

• Equal to

• Less than

What is the minimum amount you need to earn each week?

• $200

• $300

• $150

• $254

Which inequality symbol represents 'at least $254'?

• Less than

• Greater than

• Equal to

• Greater than or equal to

What is the inequality for the total hours worked?

• x + y ≤ 41

• x + y < 41

• x + y > 41

• x + y ≥ 41

What is the inequality for the total earnings?

• 5x + 8y < 254

• 5x + 8y > 254

• 5x + 8y ≥ 254

• 5x + 8y ≤ 254

What does the system of inequalities represent in this context?

• The minimum hours required

• The maximum earnings possible

• The relationship between hours and earnings

• The total number of jobs