Word Problems on Inequalities and Functions

The video tutorial by Mr. Woolley covers graphing solutions to inequalities, using various word problems to illustrate the concepts. It includes examples such as fitting cars in a garage, selling cars at a dealership, renting a car, buying clothing, purchasing concert tickets, and calculating earnings. Each problem is solved step-by-step, demonstrating how to set up and solve inequalities, graph the solutions, and interpret the results. The video concludes with instructions for practice exercises.

How do you represent the inequality m > 10 on a number line?

• A closed circle on 10, arrow to the right

• A closed circle on 10, arrow to the left

• An open circle on 10, arrow to the left

• An open circle on 10, arrow to the right

What does a closed circle on a number line indicate when graphing inequalities?

• The number is not included in the solution

• The number is included in the solution

• The inequality is strict

• The inequality is not strict

In the inequality 29 > k, what does the arrow direction indicate?

• k is not equal to 29

• k is equal to 29

• k is less than 29

• k is greater than 29

If two cars need to fit in a garage with a total width of 23.5 feet and 3.5 feet of clearance on each side, what is the maximum width of each car?

• 6.5 feet

• 7.0 feet

• 5.5 feet

• 6.0 feet

A car dealership has 525 cars and sells 50 cars per week. How many weeks will it take to have fewer than 75 cars?

• 11 weeks

• 10 weeks

• 8 weeks

• 9 weeks

If renting a car costs $25 per day plus a $75.50 insurance fee, how many days can you rent the car for a total of $525 or less?

• 18 days

• 16 days

• 15 days

• 17 days

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

• $27.50

• $25.00

• $30.00

• $28.33

If a sweater costs $28.33, what is the maximum number of sweaters Mrs. Smith can buy with $120 after buying jeans for $35?

• 2 sweaters

• 3 sweaters

• 4 sweaters

• 5 sweaters

If a concert requires at least 250 tickets and the lawn tickets are 20 fewer than balcony tickets, what is the minimum number of balcony tickets needed?

• 130

• 135

• 140

• 145

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

• 3 hours

• 4 hours

• 5 hours

• 6 hours