Solving Real-World Systems: Variable Identification & Equations

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: 14, Cows: 24, Pigs: 12

• Chickens: 18, Cows: 22, Pigs: 10

• Chickens: 5, Cows: 30, Pigs: 15

• Chickens: 20, Cows: 10, Pigs: 20

A school is planning a field trip and has 120 students attending. The number of seniors is three times the number of juniors, and the number of freshmen is 10 less than the number of seniors. How many students are in each class?

• juniors: 20, seniors: 60, freshmen: 40

• juniors: 15, seniors: 45, freshmen: 50

• juniors: 30, seniors: 90, freshmen: 20

• {"juniors": 18, "seniors": 54, "freshmen": 44}

A company produces three types of gadgets: A, B, and C. The total production is 200 gadgets. The production of type B is 20 more than type A, and type C is half the production of type B. How many gadgets of each type are produced?

• A: 60, B: 80, C: 40

• A: 40, B: 60, C: 30

• A: 30, B: 50, C: 20

• A: 50, B: 70, C: 40

In a bookstore, the total number of books is 300. The number of fiction books is three times the number of non-fiction books, and the number of reference books is 50 less than the number of fiction books. How many books of each type are there?

• Non-fiction: 30, Fiction: 90, Reference: 60

• Non-fiction: 75, Fiction: 225, Reference: 25

• Non-fiction: 100, Fiction: 200, Reference: 50

• Non-fiction: 50, Fiction: 150, Reference: 100

A concert hall has three sections: VIP, Regular, and Economy. The total number of seats is 500. The number of Regular seats is twice the number of Economy seats, and the number of VIP seats is 50 more than the number of Economy seats. How many seats are in each section?

• VIP: 100, Regular: 300, Economy: 100

• VIP: 200, Regular: 150, Economy: 50

• VIP: 150, Regular: 200, Economy: 100

• VIP: 250, Regular: 200, Economy: 50

A bakery sells three types of pastries: cakes, cookies, and pies. The total number of pastries is 150. The number of cookies is 30 more than the number of cakes, and the number of pies is half the number of cookies. How many of each type of pastry does the bakery sell?

• Cakes: 20, Cookies: 50, Pies: 80

• Cakes: 25, Cookies: 55, Pies: 40

• Cakes: 30, Cookies: 60, Pies: 30

• Cakes: 40, Cookies: 70, Pies: 20

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

• Sedans: 20, SUVs: 30, Trucks: 30

• Sedans: 15, SUVs: 40, Trucks: 25

• Sedans: 25, SUVs: 25, Trucks: 30

• Sedans: 18, SUVs: 36, Trucks: 26

A sports team has players in three positions: forwards, midfielders, and defenders. The total number of players is 45. The number of midfielders is five more than twice the number of forwards, and the number of defenders is equal to the number of forwards. How many players are in each position?

• forwards: 15, midfielders: 20, defenders: 10

• forwards: 12, midfielders: 22, defenders: 11

• {"forwards": 10, "midfielders": 25, "defenders": 10}

• forwards: 5, midfielders: 30, defenders: 10

A factory produces three products: X, Y, and Z. The total production is 600 units. The production of Y is 100 more than the production of X, and the production of Z is half the production of Y. How many units of each product are produced?

• X: 50, Y: 150, Z: 75

• X: 200, Y: 300, Z: 100

• X: 100, Y: 200, Z: 150

• X: 150, Y: 250, Z: 100

A charity organization is collecting donations in three categories: food, clothing, and money. The total number of donations is 250. The number of clothing donations is twice the number of food donations, and the number of money donations is 25 less than the number of clothing donations. How many donations are there in each category?

• Food: 70, Clothing: 140, Money: 75

• Food: 50, Clothing: 100, Money: 90

• Food: 60, Clothing: 120, Money: 70

• Food: 55, Clothing: 110, Money: 85