Contextual Systems of Equations: Interpret & Verify Solutions

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: 5, Cows: 30, Pigs: 15

• Chickens: 20, Cows: 10, Pigs: 20

• Chickens: 14, Cows: 24, Pigs: 12

• Chickens: 18, Cows: 22, Pigs: 10

A school is planning a field trip and has 120 students. The number of students in the 11th grade is three times the number of students in the 10th grade, and there are 15 more students in the 12th grade than in the 10th grade. How many students are in each grade?

• 10th_grade: 30, 11th_grade: 60, 12th_grade: 30

• 10th_grade: 20, 11th_grade: 40, 12th_grade: 50

• 10th_grade: 25, 11th_grade: 50, 12th_grade: 45

• {"10th_grade": 21, "11th_grade": 63, "12th_grade": 36}

A company produces three types of gadgets: A, B, and C. The total production is 200 gadgets. The production of type A is twice that of type B, and the production of type C is 30 less than the production of type A. How many gadgets of each type are produced?

• A: 80, B: 40, C: 50

• A: 92, B: 46, C: 62

• A: 100, B: 50, C: 70

• A: 60, B: 30, C: 40

In a concert, the total number of tickets sold is 500. The number of adult tickets sold is three times the number of child tickets, and the number of senior tickets sold is 50 less than the number of child tickets. How many tickets of each type were sold?

• Child tickets: 120, Adult tickets: 360, Senior tickets: 20

• Child tickets: 90, Adult tickets: 270, Senior tickets: 140

• Child tickets: 110, Adult tickets: 330, Senior tickets: 60

• Child tickets: 100, Adult tickets: 300, Senior tickets: 100

A bookstore sells three types of books: fiction, non-fiction, and textbooks. The total number of books sold is 300. The number of fiction books sold is twice the number of non-fiction books, and the number of textbooks sold is 50 more than the number of non-fiction books. How many of each type of book were sold?

• fiction: 50, non_fiction: 25, textbooks: 75

• fiction: 150, non_fiction: 75, textbooks: 75

• {"fiction": 100, "non_fiction": 50, "textbooks": 100}

• fiction: 200, non_fiction: 100, textbooks: 150

A factory produces three products: X, Y, and Z. The total production is 1,000 units. The production of product Y is 200 units more than product X, and the production of product Z is half that of product Y. How many units of each product are produced?

• X: 300, Y: 500, Z: 200

• X: 100, Y: 300, Z: 200

• X: 250, Y: 450, Z: 300

• X: 200, Y: 400, Z: 300

A sports team has players from three different grades: 9th, 10th, and 11th. The total number of players is 45. The number of 10th graders is twice the number of 9th graders, and there are 5 more 11th graders than 9th graders. How many players are in each grade?

• 9th graders: 12, 10th graders: 18, 11th graders: 15

• 9th graders: 5, 10th graders: 25, 11th graders: 15

• 9th graders: 15, 10th graders: 10, 11th graders: 20

• 9th graders: 10, 10th graders: 20, 11th graders: 15

A bakery sells three types of pastries: croissants, muffins, and cookies. The total number of pastries sold is 150. The number of croissants sold is three times the number of muffins, and the number of cookies sold is 20 less than the number of croissants. How many of each type of pastry were sold?

• Muffins: 50, Croissants: 150, Cookies: 100

• Muffins: 20, Croissants: 60, Cookies: 40

• Muffins: 30, Croissants: 90, Cookies: 60

• Muffins: 24, Croissants: 72, Cookies: 52

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

• cash: 6000, goods: 2000, services: 2000

• cash: 5000, goods: 2500, services: 2500

• {"cash": 4400, "goods": 2200, "services": 3400}

• cash: 3000, goods: 5000, services: 2000

A car rental company has three types of vehicles: sedans, SUVs, and trucks. The total number of vehicles is 80. The number of SUVs is three times the number of sedans, and the number of trucks is 10 less than the number of SUVs. How many vehicles of each type does the company have?

• Sedans: 20, SUVs: 40, Trucks: 20

• Sedans: 10, SUVs: 30, Trucks: 25

• Sedans: 12, SUVs: 36, Trucks: 26

• Sedans: 15, SUVs: 45, Trucks: 30