Solving Linear Inequalities: Word Problems & Graphs

A farmer has 100 acres of land 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 the farmer has a total of 120 hours of labor available, how many acres of each crop can he plant?

• 20 acres of corn and 80 acres of wheat

• 30 acres of corn and 70 acres of wheat

• 50 acres of corn and 50 acres of wheat

• 10 acres of corn and 90 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 school wants to take at least 20 students, how many students can they take without exceeding the budget?

• 25

• 10

• 0

• 30

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. The company has 30 hours of labor available. If they want to produce at least 5 Type A gadgets, how many of each type can they produce?

• 6 Type A gadgets and 5 Type B gadgets

• 5 Type A gadgets and 7 Type B gadgets

• 5 Type A gadgets and 8 Type B gadgets

• 4 Type A gadgets and 10 Type B gadgets

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 do they need to sell?

• 10 Basic and 10 Premium memberships

• 30 Basic memberships

• 20 Premium memberships

• At least 40 Basic memberships or 24 Premium memberships.

A restaurant sells two types of sandwiches: Veggie and Meat. Each Veggie sandwich costs $5 and each Meat sandwich costs $7. If the restaurant wants to make at least $200 in a day, how many of each type of sandwich do they need to sell?

• Sell at least 29 Meat sandwiches or a combination of Veggie and Meat sandwiches that meets the revenue requirement.

• Sell 15 Meat sandwiches

• Sell 10 Veggie and 10 Meat sandwiches

• Sell 20 Veggie sandwiches

A charity event is selling tickets for a concert. General admission tickets cost $10, and VIP tickets cost $25. If the charity wants to raise at least $1,000, how many of each type of ticket must they sell?

• Sell 100 general admission tickets or 40 VIP tickets, or any combination that meets the revenue requirement.

• Sell 200 general admission tickets

• Sell 50 general admission tickets and 10 VIP tickets

• Sell 30 VIP tickets and 5 general admission tickets

A clothing store sells two types of shirts: T-shirts and Dress shirts. T-shirts cost $15 each and Dress shirts cost $25 each. If the store wants to make at least $500 in sales, how many of each type of shirt do they need to sell?

• 25 T-shirts and 5 Dress shirts

• 30 T-shirts and 2 Dress shirts

• 15 T-shirts and 10 Dress shirts

• 20 T-shirts and 8 Dress shirts

A local bakery makes 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, how many cakes of each type can they bake?

• 5 Chocolate cakes and 0 Vanilla cakes, or 0 Chocolate cakes and 10 Vanilla cakes.

• 1 Chocolate cake and 8 Vanilla cakes

• 2 Chocolate cakes and 5 Vanilla cakes

• 3 Chocolate cakes and 4 Vanilla cakes

A tech company is developing two products: a smartphone and a tablet. Each smartphone requires $200 in materials and each tablet requires $150. If the company has a budget of $1,500 for materials, how many of each product can they develop?

• 6 smartphones and 2 tablets

• 7 smartphones and 1 tablet

• 5 smartphones and 3 tablets

• 4 smartphones and 4 tablets

A concert venue has a seating capacity of 500. Tickets for the front row cost $100, and tickets for the back row cost $50. If the venue wants to earn at least $30,000 from ticket sales, how many tickets of each type must they sell?

• 50 front row tickets and 450 back row tickets

• 100 front row tickets and 400 back row tickets

• 200 front row tickets and 300 back row tickets

• 150 front row tickets and 350 back row tickets