Solving Real-World Systems of Equations for 8th Graders

A local bakery sells cupcakes and cookies. If the total number of items sold is 50 and the total revenue is $200, which system of equations represents this situation?

• x + 2y = 50, x + y = 200

• x + y = 50, 3x + y = 200

• 2x + 2y = 50, x + y = 100

• x + y = 50, 2x + y = 200

A school is organizing a field trip. They have 30 students and 5 chaperones. If each student pays $10 and each chaperone pays $15, which system of equations can be used to find the total amount collected?

• x = 250 + 100

• x = 300 + 50

• x = 300 + 75

• x = 200 + 90

A farmer has chickens and cows. If he has a total of 40 animals and they have a total of 100 legs, which system of equations matches this scenario?

• x + y = 40, 3x + 4y = 100

• x + y = 40, 2x + 4y = 100

• x + y = 30, 2x + 4y = 120

• x + y = 50, 2x + 4y = 80

Two friends are saving money for a concert. One saves $5 a week and the other saves $10 a week. If they want to save a total of $100, which system of equations represents their savings?

• 5x + 5y = 100

• 5x + 10y = 100

• 10x + 5y = 100

• 5x + 15y = 100

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer pays $70, which system of equations can be used to find the number of miles driven?

• 50 + 0.20m = 70, m = m

• 50 + 0.30m = 70, m = m

• 50 + 0.20m = 50, m = m

• 70 = 50 + 0.10m, m = m

A movie theater sells adult and child tickets. If they sell 100 tickets and make $600, which system of equations can be used to find the number of adult and child tickets sold?

• x + y = 100, 15x + 3y = 600

• x + y = 80, 10x + 5y = 500

• 2x + 3y = 100, 5x + 10y = 600

• x + y = 100, 10x + 5y = 600

A store sells pencils for $0.50 each and erasers for $1.00 each. If a student buys a total of 20 items and spends $12, which system of equations represents this situation?

• {x + y = 20, 0.5x + 2y = 12}

• {x + y = 25, 0.5x + y = 15}

• {x + y = 20, 0.5x + y = 12}

• {x + y = 15, 0.5x + y = 10}

A gardener is planting flowers and shrubs. If he plants a total of 30 plants and uses 2 times as many flowers as shrubs, which system of equations can be used to find the number of each type of plant?

• 2x + y = 30, y = 3x

• x + 2y = 30, y = x

• x + y = 30, y = 2x

• x + y = 30, x = 2y

A gym has two types of memberships: monthly and yearly. If they have 200 members and collect $3000 in fees, which system of equations can be used to determine the number of each type of membership?

• x + y = 200, 30x + 300y = 3000

• x + y = 150, 20x + 200y = 2500

• x + y = 250, 30x + 300y = 4000

• x + y = 200, 25x + 250y = 3500

A bookstore sells novels and magazines. If they have a total of 150 books and the total value is $450, which system of equations matches this scenario?

• x + y = 150, 15x + 3y = 450

• x + y = 100, 10x + 5y = 300

• x + y = 150, 10x + 5y = 450

• x + y = 200, 5x + 10y = 450