Geometry and Data: Solving Systems with Unknowns

A rectangle has a length that is 3 meters longer than its width. If the perimeter of the rectangle is 30 meters, what are the dimensions of the rectangle?

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

• Width: 4 meters, Length: 7 meters

A school has three types of fruit: apples, bananas, and oranges. The total number of fruits is 120. If there are twice as many bananas as apples and 10 more oranges than bananas, how many of each type of fruit are there?

• Apples: 30, Bananas: 60, Oranges: 30

• Apples: 25, Bananas: 50, Oranges: 45

• Apples: 22, Bananas: 44, Oranges: 54

• Apples: 20, Bananas: 40, Oranges: 50

In a triangle, the first angle is twice the second angle, and the third angle is 20 degrees less than the first angle. What are the measures of the three angles?

• First angle: 80 degrees, Second angle: 40 degrees, Third angle: 60 degrees

• First angle: 90 degrees, Second angle: 45 degrees, Third angle: 70 degrees

• First angle: 60 degrees, Second angle: 30 degrees, Third angle: 40 degrees

• First angle: 70 degrees, Second angle: 35 degrees, Third angle: 50 degrees

A farmer has chickens, cows, and pigs. The total number of animals is 50. If there are 5 more cows than chickens and 2 times as many pigs as cows, how many of each animal does the farmer have?

• Chickens: 7, Cows: 12, Pigs: 24

• Chickens: 10, Cows: 15, Pigs: 20

• Chickens: 8, Cows: 13, Pigs: 22

• Chickens: 5, Cows: 10, Pigs: 30

A fruit stand sells apples, oranges, and bananas. The total number of fruits is 150. If there are 20 more apples than oranges and 10 fewer bananas than apples, how many of each fruit are there?

• Apples: 50, Oranges: 30, Bananas: 70

• Apples: 40, Oranges: 60, Bananas: 40

• Apples: 60, Oranges: 40, Bananas: 50

• Apples: 70, Oranges: 50, Bananas: 60

In a class, the number of boys is three times the number of girls. If there are 12 more boys than girls, how many boys and girls are in the class?

• 15 boys and 5 girls

• 21 boys and 7 girls

• 12 boys and 4 girls

• There are 18 boys and 6 girls in the class.

A box contains red, blue, and green marbles. The total number of marbles is 60. If there are 10 more red marbles than blue marbles and twice as many green marbles as red marbles, how many marbles of each color are there?

• Red: 20, Blue: 10, Green: 40

• Red: 30, Blue: 20, Green: 10

• Red: 25, Blue: 5, Green: 30

• Red: 15, Blue: 15, Green: 30

A bookstore has fiction, non-fiction, and children's books. The total number of books is 200. If there are 30 more fiction books than non-fiction books and 10 fewer children's books than fiction books, how many books of each type are there?

• fiction: 70, non_fiction: 60, children: 70

• {"fiction": 80, "non_fiction": 50, "children": 70}

• fiction: 90, non_fiction: 40, children: 80

• fiction: 50, non_fiction: 50, children: 60

In a garden, there are roses, tulips, and daisies. The total number of flowers is 100. If there are 20 more tulips than roses and 10 fewer daisies than tulips, how many of each type of flower are there?

• Roses: 25, Tulips: 35, Daisies: 40

• Roses: 10, Tulips: 15, Daisies: 25

• Roses: 30, Tulips: 50, Daisies: 20

• Roses: 20, Tulips: 40, Daisies: 30

A sports team has players in three positions: forwards, midfielders, and defenders. The total number of players is 18. If there are twice as many midfielders as forwards and 3 more defenders than midfielders, how many players are in each position?

• Forwards: 3, Midfielders: 6, Defenders: 9

• Forwards: 5, Midfielders: 10, Defenders: 7

• Forwards: 4, Midfielders: 8, Defenders: 6

• Forwards: 2, Midfielders: 4, Defenders: 12