Solving Real-World Problems with Linear Inequalities

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 3 hours of labor. If the farmer has a total of 240 hours of labor available, how many acres of each crop can he plant?

• 80 acres of corn and 20 acres of wheat

• 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

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 there are at least 10 students going, how many students can attend without exceeding the budget?

• 14

• 18

• 16

• 12

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

• 20

• 10

• 15

• 5

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 can they sell?

• 60 Premium memberships and 0 Basic memberships

• 30 Basic memberships and 15 Premium memberships

• The gym can sell various combinations of Basic and Premium memberships, such as 40 Basic memberships (0 Premium) or 24 Premium memberships (0 Basic), or any combination that meets the equation.

• 20 Basic memberships and 10 Premium memberships

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

• 10

• 4

• 6

• 8

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

• 250 front row tickets and 250 back row tickets

• 400 front row tickets and 100 back row tickets

• 100 front row tickets and 400 back row tickets

• 300 front row tickets and 200 back row tickets

A clothing store sells shirts and pants. Each shirt costs $20 and each pair of pants costs $30. The store has a budget of $600 for inventory. If they want to stock at least 10 shirts, how many pairs of pants can they buy?

• 10

• 13

• 12

• 15

A charity event is selling tickets for a dinner. Each ticket costs $25, and they want to raise at least $1,000. If they expect to sell at least 20 tickets, how many tickets can they sell without exceeding their goal?

• 50

• 60

• 40

• 30

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 $3,000 and wants to produce at least 5 smartphones, how many tablets can they produce?

• 8

• 13

• 15

• 10

A local theater has a maximum capacity of 300 seats. Tickets for the front section cost $15 and tickets for the back section cost $10. If the theater wants to make at least $4,000 from ticket sales, how many tickets of each section can they sell?

• 150 front section tickets and 150 back section tickets

• 200 front section tickets and 100 back section tickets

• 100 front section tickets and 200 back section tickets

• 250 front section tickets and 50 back section tickets