Exploring Real-Life Constraints: Graphing Inequalities

A farmer has 100 acres of land. He wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour of labor. If he has a total of 120 hours of labor available, how many acres of each crop can he plant?

• 30 acres of corn and 70 acres of wheat

• 20 acres of corn and 80 acres of wheat

• 10 acres of corn and 90 acres of wheat

• 50 acres of corn and 50 acres of wheat

A school is planning a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. If the number of students is represented by x, write a system of inequalities to represent the situation and determine the maximum number of students that can attend the trip.

• 10

• 12

• 18

• 14

A gym offers two types of memberships: a basic membership for $30 per month and a premium membership for $50 per month. If a customer can spend no more than $300 in a year, how many of each type of membership can they purchase?

• Up to 10 basic memberships, or up to 6 premium memberships, or combinations such as 5 premium and 1 basic.

• 3 premium and 4 basic memberships

• Up to 12 basic memberships

• Up to 8 premium memberships

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of labor and each Type B gadget requires 2 hours. If the company has 60 hours of labor available, write a system of inequalities to represent the production limits and find the maximum number of each type of gadget that can be produced.

• Maximum production is 30 gadgets (0 Type A and 30 Type B).

• Maximum production is 25 gadgets (5 Type A and 20 Type B).

• Maximum production is 15 gadgets (5 Type A and 10 Type B).

• Maximum production is 20 gadgets (10 Type A and 10 Type B).

A concert hall has a seating capacity of 500. Tickets for the front row are $50 each, and tickets for the back row are $30 each. If the total revenue from ticket sales must be at least $15,000, how many tickets of each type can be sold?

• Any combination of front row tickets (0 to 500) and back row tickets (500 to 0) that sums to 500, while ensuring total revenue is at least $15,000.

• Only front row tickets can be sold to meet the revenue requirement.

• All tickets must be sold at $50 each to achieve the revenue goal.

• A maximum of 300 tickets can be sold to reach $15,000.

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 hours to bake and each vanilla cake requires 1 hour. If the bakery has 10 hours available for baking, write a system of inequalities to represent the baking limits and determine the maximum number of cakes that can be made.

• 12

• 10

• 8

• 5

A local charity is organizing a fundraiser. They plan to sell two types of items: T-shirts for $15 each and mugs for $10 each. If they want to raise at least $1,000 and can sell no more than 100 items in total, write a system of inequalities to represent the situation and find the maximum number of each item they can sell.

• T-shirts: 80, Mugs: 20

• T-shirts: 50, Mugs: 50

• T-shirts: 66, Mugs: 34

• T-shirts: 70, Mugs: 30

A restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $12 and each non-vegetarian meal costs $15. If the restaurant wants to make at least $600 in one night and can serve no more than 50 meals, write a system of inequalities and determine the maximum number of each type of meal that can be served.

• Maximum 45 vegetarian meals or 35 non-vegetarian meals.

• Maximum 50 vegetarian meals or 40 non-vegetarian meals.

• Maximum 40 vegetarian meals or 25 non-vegetarian meals.

• Maximum 30 vegetarian meals or 20 non-vegetarian meals.

A clothing store has a sale on two types of jackets: winter jackets for $80 and rain jackets for $50. If the store wants to make at least $1,200 in sales and can sell no more than 30 jackets, write a system of inequalities to represent the situation and find the maximum number of each type of jacket that can be sold.

• Maximum winter jackets: 15, Maximum rain jackets: 15

• Maximum winter jackets: 25, Maximum rain jackets: 5

• Maximum winter jackets: 20, Maximum rain jackets: 10

• Maximum winter jackets: 10, Maximum rain jackets: 20

A pet store sells two types of pets: dogs and cats. Each dog costs $200 and each cat costs $100. If the store wants to make at least $1,500 in sales and can sell no more than 20 pets, write a system of inequalities to represent the situation and determine the maximum number of each type of pet that can be sold.

• 7 dogs and 13 cats

• 8 dogs and 12 cats

• 10 dogs and 10 cats

• 5 dogs and 15 cats