Solving Systems of Equations in Real-Life Scenarios

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges $20 plus $0.25 per mile. Write the equations in slope-intercept form and find out after how many miles the costs will be the same.

• 150 miles

• 250 miles

• 300 miles

• 200 miles

A school is selling tickets for a play. Adult tickets cost $10 each and student tickets cost $5 each. If the school wants to raise $200, write a system of equations to represent the number of adult and student tickets sold. Solve the system to find possible combinations of tickets sold.

• (25 adult, 5 student)

• (0 adult, 50 student)

• Possible combinations include (0 adult, 40 student), (5 adult, 30 student), (10 adult, 20 student), (15 adult, 10 student), (20 adult, 0 student).

• (10 adult, 30 student)

Two friends are saving money to buy a video game. Friend A saves $5 a week, while Friend B saves $3 a week. If Friend A starts with $20 and Friend B starts with $10, write the equations in slope-intercept form and determine when they will have the same amount of money.

• 1 week

• 2 weeks

• 4 weeks

• 3 weeks

A local gym offers two membership plans. Plan A costs $50 per month, while Plan B has a one-time fee of $200 and $20 per month. Write the equations for both plans and find out after how many months the costs will be equal.

• 6.67 months

• 10 months

• 5 months

• 8 months

A farmer has two types of crops: corn and wheat. He earns $3 per bushel of corn and $2 per bushel of wheat. If he wants to earn at least $120, write a system of equations to represent the situation and solve for the number of bushels of each crop he needs to sell.

• The farmer can earn $120 by selling 30 bushels of corn and 15 bushels of wheat.

• The farmer needs to sell 60 bushels of corn and 10 bushels of wheat.

• The farmer needs to sell at least 40 bushels of corn (x=40, y=0) or any combination that satisfies 3x + 2y >= 120.

• The farmer must sell exactly 50 bushels of corn to meet his goal.

A bookstore sells novels for $15 each and textbooks for $25 each. If they want to make at least $300 in sales, write a system of equations to represent the number of novels and textbooks sold. Solve the system to find possible combinations of books sold.

• (5, 5)

• Possible combinations include (0, 12), (5, 9), (10, 6), (15, 3), (20, 0) and other combinations where 15x + 25y >= 300.

• (10, 0)

• (0, 10)

A pizza shop sells small pizzas for $8 and large pizzas for $12. If they want to make $240 in one day, write a system of equations to represent the number of small and large pizzas sold. Solve the system to find possible combinations of pizzas sold.

• Possible combinations include (0, 20), (3, 16), (6, 12), (9, 8), (12, 4), (15, 0).

• (5, 15)

• (10, 10)

• (2, 18)

A charity is selling cookies and brownies. Each cookie sells for $2 and each brownie for $3. If they want to raise at least $150, write a system of equations to represent the number of cookies and brownies sold. Solve the system to find possible combinations of treats sold.

• Possible combinations include (0, 50), (15, 30), (30, 10), (75, 0) and others where x >= 0 and y >= 0.

• (50, 25)

• (10, 40)

• (20, 20)

A bike rental shop charges a flat fee of $15 plus $5 per hour. Another shop charges $10 plus $7 per hour. Write the equations in slope-intercept form and find out after how many hours the costs will be the same.

• 2.5 hours

• 4.5 hours

• 1 hour

• 3 hours