Solving Systems of Equations: Relationships and Accuracy

A farmer has chickens, cows, and pigs. The total number of animals is 50. The number of cows is twice the number of pigs, and the number of chickens is 10 less than the number of cows. How many of each type of animal does the farmer have?

• Chickens: 18, Cows: 22, Pigs: 10

• Chickens: 5, Cows: 30, Pigs: 15

• Chickens: 20, Cows: 10, Pigs: 20

• Chickens: 14, Cows: 24, Pigs: 12

In a school, there are students enrolled in art, music, and drama. The total number of students is 120. The number of students in music is three times the number of students in art, and the number of students in drama is 20 less than the number of students in music. How many students are in each program?

• Art: 30, Music: 90, Drama: 0

• Art: 20, Music: 60, Drama: 40

• Art: 50, Music: 10, Drama: 60

• Art: 40, Music: 20, Drama: 60

A bookstore sells fiction, non-fiction, and magazines. The total sales for the day were $500. Fiction sales were $100 more than non-fiction, and magazine sales were half of the non-fiction sales. How much did each category sell?

• Fiction: $200, Non-Fiction: $100, Magazines: $200

• Fiction: $300, Non-Fiction: $200, Magazines: $100

• Fiction: $250, Non-Fiction: $150, Magazines: $100

• Fiction: $400, Non-Fiction: $300, Magazines: $50

A sports team has players in basketball, soccer, and baseball. The total number of players is 30. There are twice as many soccer players as basketball players, and the number of baseball players is 5 less than the number of soccer players. How many players are in each sport?

• Basketball: 10, Soccer: 15, Baseball: 5

• Basketball: 5, Soccer: 10, Baseball: 12

• Basketball: 8, Soccer: 16, Baseball: 6

• Basketball: 7, Soccer: 14, Baseball: 9

In a factory, there are machines producing A, B, and C products. The total production is 200 units. Product A is produced at a rate of 3 times that of product B, and product C is produced at a rate of 10 units less than product A. How many units of each product are produced?

• A: 90, B: 30, C: 80

• A: 70, B: 40, C: 90

• A: 100, B: 50, C: 60

• A: 80, B: 20, C: 70

A concert has tickets for VIP, regular, and student sections. The total number of tickets sold is 300. VIP tickets sold are 50 more than regular tickets, and student tickets sold are half of the regular tickets. How many tickets were sold in each section?

• VIP: 200, Regular: 100, Student: 0

• VIP: 120, Regular: 80, Student: 60

• {"VIP": 150, "Regular": 100, "Student": 50}

• VIP: 100, Regular: 150, Student: 50

A recipe requires flour, sugar, and butter. The total weight of the ingredients is 2 kg. The weight of the flour is 500 grams more than the sugar, and the butter weighs 200 grams less than the sugar. How much does each ingredient weigh?

• Flour: 800 grams, Sugar: 300 grams, Butter: 400 grams

• Flour: 1066.67 grams, Sugar: 566.67 grams, Butter: 366.67 grams

• Flour: 1200 grams, Sugar: 700 grams, Butter: 500 grams

• Flour: 900 grams, Sugar: 600 grams, Butter: 500 grams

In a garden, there are roses, tulips, and daisies. The total number of flowers is 80. The number of tulips is twice the number of roses, and the number of daisies is 10 less than the number of tulips. How many of each type of flower are there?

• Roses: 20, Tulips: 40, Daisies: 30

• Roses: 18, Tulips: 36, Daisies: 26

• Roses: 15, Tulips: 30, Daisies: 25

• Roses: 10, Tulips: 20, Daisies: 15

A car rental company has economy, standard, and luxury cars. The total number of cars is 150. The number of standard cars is 20 more than the economy cars, and the luxury cars are half the number of standard cars. How many cars are in each category?

• Economy: 50, Standard: 70, Luxury: 30

• Economy: 30, Standard: 50, Luxury: 40

• Economy: 45, Standard: 55, Luxury: 50

• Economy: 40, Standard: 60, Luxury: 30

A charity event has donations from three sources: individuals, businesses, and organizations. The total donations amount to $10,000. Donations from businesses are $2,000 more than from individuals, and donations from organizations are $1,000 less than from businesses. How much was donated by each source?

• Individuals: 2000, Businesses: 4000, Organizations: 4000

• Individuals: 2500, Businesses: 4500, Organizations: 3000

• Individuals: 3000, Businesses: 5000, Organizations: 2000

• {"Individuals": 2333.33, "Businesses": 4333.33, "Organizations": 3333.33}