4.2 Budgeting & Linear Inequalities Quiz

What are the differences between a linear inequality and a linear equation?

• Linear inequality has variables on both sides, while a linear equation has variables on one side.

• Linear inequality represents constraints, while a linear equation represents a specific relationship.

• Linear inequality has a shaded area on the graph and may have either a solid or dashed line, while a linear equation has a solid straight line.

• Linear inequality uses an inequality sign, while a linear equation always uses an equals sign.

You needs to earn at least $770 per week, working part-time as a cashier for $11 per hour and earning $35 per hour doing freelance event photography.

Which of the following represents the inequality for earning at least $770 per week by working as a cashier and doing freelance event photography?

• 11x + 35y > 770

• 11x + 35y ≥ 770

• 20x - y > 770

• 20x - y ≥ 770

Nathan needs to earn at least $880 per week.

He works as an Uber driver, earning an average of $16 per hour, and as a tutor, earning $20 per hour. Let x represent hours driving and y represents hours tutoring.

Which inequality represents the scenario where Nathan wants to work at most 50 hours per week?

• x + y < 50

• x + y ≤ 50

• 16x + 20y ≤ 50

• 16x + 20y < 50

Nathan needs to earn at least $880 per week.

He works as an Uber driver, earning an average of $16 per hour, and as a tutor, earning $20 per hour.

Write an inequality to represent this situation, where x represents hours driving and y represents hours tutoring.

• 16x + 20y < 880

• 16x + 20y ≥ 880

• 16x + 20y ≤ 880

• 16x + 20y > 880

Nathan needs to earn at least $880 per week.

He works as an Uber driver, earning an average of $16 per hour, and as a tutor, earning $20 per hour.

6. Is there any way Nathan can earn at least $880 while working 50 hours or less?

• Yes, there scenarios where he can work between 44-50 hours a week and earn at least $880 by working as a tutor.

• No, there is no combination of hours that he would earn at least $880 between both jobs with only 50 hours a week.

• Inconclusive, there is not enough information

• He can get at least $880 by working the jobs because the money will just magically appear if he wishes hard enough.

Noel is a waiter in a restaurant who is paid the federal minimum wage for tipped workers: $2.13. They also keep 70% of the tips left by their tables. So, they always earn at least $2.13 per hour, but their actual earnings vary.

Write an inequality to represent Noel’s earnings, y, if they work x hours.

• y ≥ 2.13x

• y < 2.13x

• y > 2.13x

• y ≤ 2.13x

Yvonne works part-time in customer service earning $20 per hour. She also earns $15 per hour working in childcare.

She wants to earn at least $750 each week.

Which of the following inequalities describes her situation?

• 15x + 20 y < 750

• 15x + 20y ≤ 750

• 15x + 20y ≥ 750

• 15x + 20y > 750

Yvonne works part-time in customer service earning $20 per hour. She also earns $15 per hour working in childcare.

She wants to earn at least $750 each week.

Which of the following graphs describes her situation?

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Sana works part-time in event management earning $20 per hour. She also does freelance carpentry projects for $25 per hour.

Which inequality represents the scenario where Sana covers her basic expenses with $750, but wants to save up for a vacation?

• 20x + 25y > 750

• 20x + 25y < 750

• 20x + 25y ≤ 750

• 20x + 25y ≥ 750

Sana works part-time in event management earning $20 per hour. She also does freelance carpentry projects for $25 per hour.

She wants to earn more than $750 per week.

What is the fewest number of hours that Sana could work and still earn more than $750?

Justify your response.

• 30 hours.  

  Sana makes more money in event management.  If she dedicated all of her work time to that job, she would reach $750 in the fewest number of hours.

• 38 hours.  

  Sana makes more money in event management.  If she dedicated all of her work time to that job, she would reach $750 in the fewest number of hours.

• 38 hours.  

  Sana makes more money in freelance carpentry.  If she dedicated all of her work time to that job, she would reach $750 in the fewest number of hours.

• 30 hours.  

  Sana makes more money in freelance carpentry.  If she dedicated all of her work time to that job, she would reach $750 in the fewest number of hours.