Inequalities and Problem Solving

Mr. Hulk presents Lesson 15 on solving inequalities through various exercises. The lesson covers practical applications such as fitting cars in a garage, selling cars at a dealership, renting a car, buying clothes, purchasing concert tickets, and earning money for downloads. Each exercise involves setting up and solving inequalities, graphing solutions, and interpreting results in real-world contexts.

What is the maximum width each car can have to fit into the garage with the required clearance?

• 6.0 feet

• 7.0 feet

• 6.5 feet

• 5.5 feet

How is the inequality represented on a number line when the solution is less than or equal to a certain value?

• Open circle with arrow to the right

• Closed circle with arrow to the right

• Closed circle with arrow to the left

• Open circle with arrow to the left

If a dealership has 525 cars and sells 50 cars per week, how many weeks will it take to have fewer than 75 cars?

• 11 weeks

• 8 weeks

• 9 weeks

• 10 weeks

What is the inequality setup for determining the number of weeks to sell cars at a dealership?

• 525 - 50W < 75

• 525 + 50W < 75

• 525 + 50W > 75

• 525 - 50W > 75

What is the maximum number of days a car can be rented if the total cost must not exceed $525, given a daily rate and a one-time fee?

• 19 days

• 16 days

• 17 days

• 18 days

In the car rental problem, what does the term 'no more than' translate to in inequality terms?

• Greater than

• Less than

• Less than or equal to

• Greater than or equal to

If Mrs. Smith has $120 and buys jeans for $35, what is the maximum price she can pay for each of the three sweaters?

• $30.00

• $28.33

• $27.67

• $29.00

How many balcony tickets must be bought if the total number of tickets is at least 250 and there are 20 fewer lawn tickets than balcony tickets?

• 130

• 135

• 140

• 145

Samuel needs $29 and earns $6 per hour plus a $5 allowance. How many hours must he work to meet his goal?

• 3 hours

• 4 hours

• 5 hours

• 6 hours

What is the key consideration when graphing the solution to an inequality involving ticket sales?

• The number of tickets must be zero

• The number of tickets must be a fraction

• The number of tickets must be an integer

• The number of tickets can be negative