Solving Systems of Equations: Animal Counts & Ticket Sales

A farmer has chickens, cows, and pigs. The total number of animals is 50. The total number of legs is 140. If the number of cows is twice the number of pigs, how many of each animal does the farmer have?

• Chickens: 5, Cows: 30, Pigs: 15

• Chickens: 10, Cows: 40, Pigs: 20

• Chickens: 20, Cows: 10, Pigs: 5

• Chickens: 15, Cows: 25, Pigs: 10

A school is planning a field trip. They have 3 types of tickets: student tickets, adult tickets, and senior tickets. The total number of tickets sold is 200. The total revenue from ticket sales is $1500. If the price of a student ticket is $5, an adult ticket is $10, and a senior ticket is $7, how many of each type of ticket were sold?

• 60 student tickets, 80 adult tickets, 60 senior tickets

• 40 student tickets, 120 adult tickets, 40 senior tickets

• 70 student tickets, 70 adult tickets, 60 senior tickets

• 50 student tickets, 100 adult tickets, 50 senior tickets

A company produces three types of products: A, B, and C. The total production is 300 units. The total profit from these products is $1200. If product A contributes $4 to the profit, product B contributes $5, and product C contributes $3, how many units of each product were produced?

• Product A: 100 units, Product B: 100 units, Product C: 100 units

• Product A: 0 units, Product B: 150 units, Product C: 150 units

• Product A: 50 units, Product B: 200 units, Product C: 50 units

• Product A: 150 units, Product B: 0 units, Product C: 150 units

In a concert, there are three types of tickets: VIP, regular, and student. The total number of tickets sold is 500. The total revenue is $8000. If VIP tickets cost $50, regular tickets cost $20, and student tickets cost $10, how many of each type of ticket were sold?

• VIP: 70, Regular: 80, Student: 350

• VIP: 50, Regular: 100, Student: 350

• VIP: 100, Regular: 200, Student: 200

• VIP: 30, Regular: 150, Student: 320

A bakery sells three types of pastries: croissants, muffins, and cookies. The total number of pastries sold is 120. The total revenue from sales is $360. If croissants are sold for $3 each, muffins for $2 each, and cookies for $1 each, how many of each type were sold?

• 50 croissants, 30 muffins, 40 cookies

• 70 croissants, 20 muffins, 30 cookies

• 40 croissants, 40 muffins, 40 cookies

• 60 croissants, 0 muffins, 60 cookies

A car rental company has three types of cars: sedans, SUVs, and trucks. The total number of cars rented is 80. The total revenue from rentals is $2400. If sedans cost $30 per day, SUVs cost $50 per day, and trucks cost $70 per day, how many of each type of car was rented?

• 50 sedans, 20 SUVs, 10 trucks

• 30 sedans, 30 SUVs, 20 trucks

• 40 sedans, 40 SUVs, 0 trucks

• 20 sedans, 50 SUVs, 10 trucks

A bookstore sells three types of books: fiction, non-fiction, and children's books. The total number of books sold is 200. The total revenue is $1500. If fiction books are sold for $15, non-fiction for $20, and children's books for $10, how many of each type were sold?

• 100 fiction, 100 non-fiction, 0 children's books

• 50 fiction, 50 non-fiction, 100 children's books

• 0 fiction, 100 non-fiction, 100 children's books

• 100 fiction, 0 non-fiction, 100 children's books

A sports team has three types of players: forwards, midfielders, and defenders. The total number of players is 22. The total number of goals scored by all players is 50. If forwards score an average of 3 goals each, midfielders score 2 goals each, and defenders score 1 goal each, how many players are in each position?

• 8 forwards, 10 midfielders, 4 defenders

• 9 forwards, 9 midfielders, 4 defenders

• 10 forwards, 8 midfielders, 4 defenders

• 11 forwards, 6 midfielders, 5 defenders

A factory produces three types of gadgets: X, Y, and Z. The total production is 500 gadgets. The total cost of production is $3000. If gadget X costs $5 to produce, gadget Y costs $7, and gadget Z costs $4, how many of each gadget were produced?

• 100 gadgets of X, 200 gadgets of Y, and 200 gadgets of Z

• 300 gadgets of X, 100 gadgets of Y, and 100 gadgets of Z

• 150 gadgets of X, 250 gadgets of Y, and 100 gadgets of Z

• 200 gadgets of X, 300 gadgets of Y, and 0 gadgets of Z

A charity event has three types of donations: cash, goods, and services. The total number of donations is 150. The total value of donations is $5000. If cash donations are valued at $50 each, goods at $30 each, and services at $20 each, how many of each type of donation were received?

• Cash: 25, Goods: 25, Services: 100

• Cash: 20, Goods: 40, Services: 90

• Cash: 10, Goods: 60, Services: 80

• Cash: 30, Goods: 50, Services: 70