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?

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?

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?

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?

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?

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?

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?

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?

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?

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?