Translate Real-World Scenarios into Equations: Grade 8

A school is selling tickets for a play. Adult tickets cost $10 each and student tickets cost $5 each. If they sold a total of 50 tickets for $400, write a system of equations to represent this situation. Identify the variables.

• x + y = 50, 10x + 5y = 400

• x + y = 50, 5x + 10y = 400

• x + y = 60, 10x + 5y = 500

• x + y = 40, 10x + 5y = 300

Maria has twice as many apples as John. Together, they have 30 apples. Create a system of equations to model this scenario and identify the variables involved.

• J = 20, M = 10

• J = 15, M = 15

• J = 10, M = 20 where J is John's apples and M is Maria's apples.

• J = 5, M = 25

A car rental company charges a flat fee of $20 plus $0.50 per mile driven. If a customer paid $45 for a rental, write a system of equations to represent the situation and identify the variables.

• C = 20 + 0.50x; C = 45

• C = 20 + 0.75x; C = 45

• C = 30 + 0.50x; C = 45

• C = 20 + 0.25x; C = 50

In a fruit basket, there are oranges and bananas. If there are 12 fruits in total and the number of oranges is 3 more than the number of bananas, create a system of equations to represent this situation. Identify the variables.

• x + y = 12, y = x + 3

• x + y = 15, y = x + 5

• x + y = 10, y = x - 3

• x - y = 12, y = x + 3

A bookstore sells novels for $15 each and magazines for $5 each. If a customer buys a total of 10 items for $100, write a system of equations to represent this situation and identify the variables.

• x + y = 5, 15x + 5y = 75

• x + y = 10, 10x + 2y = 100

• x + y = 15, 15x + 5y = 50

• x + y = 10, 15x + 5y = 100

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $5 each week, while Jamie saves $10 each week. If they want to save a total of $100 together, create a system of equations to model this situation and identify the variables.

• 5x + 5y = 100, where x = weeks Alex saves, y = weeks Jamie saves.

• 5x + 10y = 100, where x = weeks Alex saves, y = weeks Jamie saves.

• 5x + 15y = 100, where x = weeks Alex saves, y = weeks Jamie saves.

• 10x + 5y = 100, where x = weeks Alex saves, y = weeks Jamie saves.

A gardener is planting flowers and shrubs. If the total number of plants is 30 and the number of flowers is 5 more than twice the number of shrubs, write a system of equations to represent this situation. Identify the variables involved.

• x + y = 30, y = 2x + 5

• x + y = 25, y = 2x - 5

• x + y = 30, y = 3x + 5

• x + y = 30, y = 2x - 5

A local gym offers a monthly membership for $30 and a per-visit fee of $5. If a member paid $75 in total, write a system of equations to represent this situation and identify the variables.

• 25x + 10y = 75, x >= 1

• 30x + 2y = 75, y >= 0

• 30x + 5y = 75, x >= 1

• 20x + 5y = 75, x >= 0

In a classroom, there are boys and girls. If there are 24 students in total and the number of girls is 4 more than the number of boys, create a system of equations to represent this situation. Identify the variables involved.

• b + g = 24; g = b + 6

• b + g = 20; g = b - 4

• b + g = 24; g = b + 4

• b + g = 30; g = b + 2

A pet store has cats and dogs. If there are 20 pets in total and the number of cats is 3 less than the number of dogs, write a system of equations to represent this situation and identify the variables.

• x + y = 15, y = x - 5

• x + y = 20, y = x - 3

• x - y = 20, y = x + 3

• x + y = 25, y = x + 3