Real-Life Linear Inequalities: Word Problems & Graphs

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 3 hours. If he has a total of 240 hours of labor available, how many acres of each crop can he plant? Graph the inequalities and find the feasible region.

• 40 acres of corn and 60 acres of wheat

• 50 acres of corn and 50 acres of wheat

• The farmer can plant 60 acres of corn and 0 acres of wheat, or 0 acres of corn and 80 acres of wheat, or a combination such as 30 acres of corn and 30 acres of wheat.

• 70 acres of corn and 10 acres of wheat

A school is organizing a field trip. The cost per student is $20 for transportation and $15 for food. If the school has a budget of $600, how many students can attend the trip? Create a graph to represent the situation and identify the maximum number of students.

• 15

• 20

• 25

• 17

A company produces two types of gadgets: A and B. Each gadget A requires 4 hours of labor and each gadget B requires 2 hours. The company has 40 hours of labor available. If they want to produce at least 5 gadgets A, how many of each type can they produce? Graph the inequalities and find the solution set.

• Maximum 8 gadgets A and 4 gadgets B

• Maximum 5 gadgets A and 5 gadgets B

• Maximum 10 gadgets A and 0 gadgets B, or 5 gadgets A and 10 gadgets B.

• Maximum 6 gadgets A and 12 gadgets B

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, and the premium costs $50. If a customer can spend no more than $200 per month, how many of each type of membership can they purchase? Illustrate this with a graph and determine the possible combinations.

• (1, 4)

• (2, 3)

• Possible combinations of memberships are: (0, 4), (1, 3), (2, 2), (3, 1), (4, 0), (5, 0) with varying basic memberships.

• (0, 5)

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 3 eggs and each vanilla cake requires 2 eggs. If the bakery has 30 eggs, how many cakes of each type can they make? Graph the inequalities and find the feasible solutions.

• 15 chocolate cakes and 0 vanilla cakes

• The bakery can make a maximum of 10 chocolate cakes and 0 vanilla cakes, or various combinations such as 0 chocolate and 15 vanilla cakes.

• 5 chocolate cakes and 10 vanilla cakes

• 8 chocolate cakes and 4 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 total revenue from ticket sales must be at least $15,000, how many tickets of each type can be sold? Create a graph to visualize the constraints and find the solution set.

• 100 front row tickets and 400 back row tickets

• 300 front row tickets and 200 back row tickets

• 400 front row tickets and 100 back row tickets

• 250 front row tickets and 250 back row tickets

A clothing store sells shirts and pants. Each shirt costs $20 and each pair of pants costs $30. If a customer has a budget of $300, how many shirts and pants can they buy? Graph the inequalities and determine the combinations that fit within the budget.

• The customer can buy combinations of shirts and pants such as (0, 10), (1, 9), (2, 8), ..., (10, 0) within the budget.

• (3, 7)

• (15, 0)

• (5, 5)

A charity event is selling two types of tickets: regular and VIP. Regular tickets cost $25, and VIP tickets cost $50. If the total revenue needs to be at least $2,000, how many of each type of ticket must be sold? Illustrate this with a graph and find the feasible solutions.

• Sell at least 80 regular tickets, or combinations of regular and VIP tickets that satisfy 25x + 50y >= 2000.

• Sell 60 regular tickets and 10 VIP tickets

• Sell 100 VIP tickets only

• Sell 40 regular tickets and 20 VIP tickets

A tech company is developing two products: software and hardware. Each software product requires 5 hours of development, and each hardware product requires 3 hours. If the team has 60 hours available, how many of each product can they develop? Graph the inequalities and identify the feasible region.

• The team can develop 8 software products and 5 hardware products.

• The team can develop a maximum of 12 software products or a combination of software and hardware products such as 6 software and 10 hardware.

• The team can develop 15 software products and 5 hardware products.

• The team can develop 20 hardware products only.

A restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $10 and each non-vegetarian meal costs $15. If the restaurant wants to make at least $1,000 in a week, how many meals of each type should they sell? Create a graph to represent the situation and find the solution set.

• Selling 50 vegetarian meals and 20 non-vegetarian meals is sufficient.

• The restaurant should sell only vegetarian meals to meet the goal.

• The restaurant needs to sell 100 meals of any type to reach $1,000.

• The restaurant should sell combinations of vegetarian and non-vegetarian meals such that 10x + 15y >= 1000.