Solving Systems of Equations with Three Variables

A farmer has three types of crops: corn, wheat, and soybeans. He wants to plant a total of 120 acres. If he plants 2 acres of corn for every acre of wheat and 3 acres of soybeans for every acre of corn, how many acres of each crop will he plant?

• Corn: 40 acres, Wheat: 20 acres, Soybeans: 60 acres

• Corn: 26.67 acres, Wheat: 13.33 acres, Soybeans: 80 acres

• Corn: 20 acres, Wheat: 10 acres, Soybeans: 90 acres

• Corn: 30 acres, Wheat: 15 acres, Soybeans: 75 acres

A school is organizing a field trip for three grades: 8th, 9th, and 10th. The total number of students going is 150. If there are twice as many 9th graders as 8th graders and three times as many 10th graders as 9th graders, how many students from each grade are attending?

• {"8th": 16, "9th": 32, "10th": 96}

• 8th: 15, 9th: 25, 10th: 110

• 8th: 20, 9th: 40, 10th: 90

• 8th: 10, 9th: 30, 10th: 110

A toy store sells three types of toys: dolls, cars, and puzzles. The total revenue from selling these toys is $500. If dolls sell for $10 each, cars for $15 each, and puzzles for $5 each, and the store sells twice as many dolls as cars and three times as many puzzles as dolls, how many of each toy did they sell?

• 10 dolls, 5 cars, 30 puzzles

• 8 dolls, 4 cars, 20 puzzles

• 12 dolls, 6 cars, 25 puzzles

• 5 dolls, 10 cars, 15 puzzles

In a bakery, three types of pastries are made: croissants, muffins, and scones. The total number of pastries made is 200. If the number of croissants is three times the number of muffins and the number of scones is 50 less than the number of croissants, how many of each type of pastry were made?

• Muffins: 50, Croissants: 100, Scones: 50

• Muffins: 30, Croissants: 90, Scones: 70

• Muffins: 35, Croissants: 105, Scones: 55

• Muffins: 40, Croissants: 120, Scones: 60

A concert has three ticket types: VIP, regular, and student. The total number of tickets sold is 300. If there are twice as many regular tickets as VIP tickets and three times as many student tickets as regular tickets, how many tickets of each type were sold?

• VIP: 30, Regular: 60, Student: 180

• VIP: 60, Regular: 120, Student: 180

• VIP: 20, Regular: 40, Student: 240

• VIP: 50, Regular: 100, Student: 150

A bookstore has three sections: fiction, non-fiction, and children's books. The total number of books is 600. If there are twice as many fiction books as non-fiction books and three times as many children's books as fiction books, how many books are in each section?

• Non-fiction: 100, Fiction: 200, Children's: 300

• Non-fiction: 50, Fiction: 100, Children's: 450

• Non-fiction: 67, Fiction: 134, Children's: 399

• Non-fiction: 80, Fiction: 160, Children's: 360

A gym offers three types of memberships: basic, premium, and family. The total number of memberships sold is 250. If there are twice as many premium memberships as basic memberships and three times as many family memberships as premium memberships, how many memberships of each type were sold?

• 30 basic, 60 premium, 160 family

• 28 basic, 56 premium, 166 family

• 40 basic, 80 premium, 130 family

• 25 basic, 50 premium, 175 family

A factory produces three products: A, B, and C. The total production is 1,000 units. If the production of product A is twice that of product B and the production of product C is 100 units less than that of product A, how many units of each product are produced?

• A: 300, B: 150, C: 200

• A: 500, B: 250, C: 250

• A: 440, B: 220, C: 340

• A: 400, B: 300, C: 200

A charity event has three types of donations: cash, goods, and services. The total value of donations is $10,000. If cash donations are three times the value of goods and services are $1,000 less than cash donations, how much was donated in each category?

• Goods: $1000, Cash: $5000, Services: $4000

• Goods: $3000, Cash: $7000, Services: $0

• Goods: $2000, Cash: $6000, Services: $2000

• Goods: $1571.43, Cash: $4714.29, Services: $3714.29

A pet store has three types of animals: dogs, cats, and birds. The total number of animals is 90. If there are twice as many cats as dogs and three times as many birds as cats, how many of each type of animal does the store have?

• 15 dogs, 30 cats, 45 birds

• 5 dogs, 10 cats, 75 birds

• 20 dogs, 10 cats, 60 birds

• 10 dogs, 20 cats, 60 birds