Inequalities in Real Life: Word Problems and Graphs

A farmer has 100 meters of fencing to create a rectangular pen for his animals. If the length of the pen is represented by x and the width by y, write an inequality to represent the maximum area of the pen. What are the possible values for x and y?

• x + y = 50, 0 < x < 50, 0 < y < 50

• x + y ≥ 50, 0 < x < 50, 0 < y < 50

• x + y < 100, 0 < x ≤ 100, 0 < y ≤ 100

• x + y ≤ 50, 0 < x ≤ 50, 0 < y ≤ 50

A school is planning a field trip and has a budget of $500. The cost per student is $20, and the bus rental is $200. Write an inequality to represent the maximum number of students that can attend the trip. How many students can they take?

• 15

• 25

• 20

• 10

A local gym has a membership limit of 150 members. If x represents the number of adult members and y represents the number of youth members, write an inequality to represent the membership limit. What combinations of adult and youth members are possible?

• x + y = 150, where x > 0 and y > 0.

• x + y ≤ 150, where x ≥ 0 and y ≥ 0.

• x + y < 150, where x ≥ 0 and y ≥ 0.

• x + y ≥ 150, where x ≤ 0 and y ≤ 0.

A concert venue can hold a maximum of 300 people. If tickets for adults cost $15 and tickets for children cost $10, and the total revenue must be at least $2000, write an inequality to represent this situation. How many adults and children can attend?

• x + y < 300 and 15x + 10y < 2000

• x + y ≥ 300 and 15x + 10y ≤ 2000

• x + y ≤ 300 and 15x + 10y = 2000

• x + y ≤ 300 and 15x + 10y ≥ 2000

A pizza shop sells large pizzas for $12 and medium pizzas for $8. If the shop wants to make at least $300 in sales, write an inequality to represent the number of large (x) and medium (y) pizzas they need to sell. What are some possible combinations?

• 8x + 12y > 300

• 15x + 10y <= 300

• 12x + 8y >= 300; Possible combinations include (x=0, y=37.5), (x=10, y=15), (x=20, y=0).

• 10x + 5y >= 300

A charity event aims to raise at least $1000. If each ticket sold for adults is $25 and for children is $15, write an inequality to represent the total number of adult (x) and child (y) tickets that need to be sold. What combinations can achieve this goal?

• 25x + 20y >= 1000

• 30x + 20y >= 1000

• 20x + 10y >= 1000

• 25x + 15y >= 1000

A factory produces two types of toys: type A and type B. Each type A toy requires 2 hours to make, and each type B toy requires 3 hours. If the factory has 60 hours available, write an inequality to represent the production limit. What combinations of toys can be produced?

• 2x + 3y < 60, where x, y ≥ 0.

• x + y ≤ 20, where x, y ≥ 0.

• 2x + 3y = 60, where x, y ≥ 0.

• 2x + 3y ≤ 60, where x, y ≥ 0.

A bookstore has a sale where they offer a discount on books. If the total number of books sold must be at least 50 and the number of fiction books (x) plus non-fiction books (y) cannot exceed 100, write the inequalities that represent this situation. What are the possible values for x and y?

• 50 <= x + y <= 100

• x + y < 50

• x + y > 100

• x + y = 50

A bakery can produce a maximum of 200 loaves of bread in a day. If each loaf of whole wheat bread requires 1 hour to bake and each loaf of sourdough requires 2 hours, write an inequality to represent the baking time. What combinations of loaves can be baked?

• x + 2y ≤ 300 and x + y ≤ 300

• x + 2y ≤ 200 and x + y ≤ 150

• x + y ≤ 100 and x + 2y ≤ 100

• The combinations of loaves (x, y) must satisfy x + 2y ≤ 200 and x + y ≤ 200, where x ≥ 0 and y ≥ 0.

A sports team has a budget of $1500 for new equipment. If they want to buy basketballs for $30 each and soccer balls for $20 each, write an inequality to represent the maximum number of each type of ball they can purchase. What combinations fit within the budget?

• The inequality is 30x + 20y ≤ 1000. Combinations include (0, 50), (10, 40), (20, 30) and others.

• The inequality is 30x + 20y ≥ 1500. Combinations include (0, 100), (5, 70), (15, 40) and others.

• The inequality is 30x + 20y = 1500. Combinations include (50, 0), (0, 75), (25, 25) and others.

• The inequality is 30x + 20y ≤ 1500. Combinations include (0, 75), (10, 60), (20, 45), (30, 30), (40, 15), (50, 0) and others within the constraints.