Solving Real-Life Linear Inequalities: Grade 9 Challenges

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 160 hours of labor available, how many acres of each crop can he plant?

• 50 acres of corn and 50 acres of wheat

• 70 acres of corn and 30 acres of wheat

• 60 acres of corn and 40 acres of wheat

• 80 acres of corn and 20 acres of wheat

A school is organizing 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.

• 14

• 12

• 18

• 10

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of assembly and each Type B requires 2 hours. The company has 24 hours of assembly time available. If they want to produce at least 4 Type A gadgets, how many Type B gadgets can they produce?

• 10

• 8

• 4

• 6

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, and the premium membership costs $50 per month. If the gym wants to earn at least $1,200 in a month, how many of each type of membership must they sell?

• At least 40 basic memberships or 24 premium memberships, or a combination of both.

• At least 10 basic memberships or 60 premium memberships.

• At least 30 basic memberships or 20 premium memberships.

• At least 50 basic memberships or 15 premium memberships.

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 cups of flour and each vanilla cake requires 3 cups. If the bakery has 30 cups of flour, how many cakes of each type can they make if they want to make at least 5 chocolate cakes?

• 4 chocolate cakes and 7 vanilla cakes

• 5 chocolate cakes and 5 vanilla cakes

• 6 chocolate cakes and 4 vanilla cakes

• 5 chocolate cakes and 6 vanilla cakes

A concert hall has a seating capacity of 500. Tickets for the front row cost $50, and tickets for the back row cost $30. If the concert hall wants to make at least $15,000 from ticket sales, how many tickets of each type must they sell?

• 250 front row tickets and 250 back row tickets

• 300 front row tickets and 200 back row tickets

• 100 front row tickets and 400 back row tickets

• 400 front row tickets and 100 back row tickets

A clothing store sells shirts and pants. Each shirt costs $20 and each pair of pants costs $30. If the store wants to make at least $1,000 in sales and has a maximum of 50 items to sell, how many shirts and pants can they sell?

• 30 shirts and 20 pants

• 25 shirts and 25 pants

• 40 shirts and 10 pants

• 10 shirts and 40 pants

A charity event is selling tickets for a dinner. Each ticket costs $25, and they want to raise at least $2,500. If they can sell a maximum of 150 tickets, how many tickets must they sell to meet their goal?

• 75

• 150

• 125

• 100

A local theater has a maximum seating capacity of 200. They sell tickets for $15 for adults and $10 for children. If they want to make at least $1,500 from ticket sales, how many adult and child tickets can they sell?

• 50 adult tickets and 150 child tickets

• 70 adult tickets and 130 child tickets

• 80 adult tickets and 120 child tickets

• 60 adult tickets and 140 child tickets

A pet store has a limit of 50 animals it can house. They have dogs and cats. Each dog takes up 2 spaces and each cat takes up 1 space. If the store wants to have at least 10 dogs, how many cats can they have?

• 20

• 25

• 30

• 35