Systems of Equations: Saving Money and Graphing Skills

Maria has $50 to spend on notebooks and pens. Notebooks cost $5 each and pens cost $2 each. Write a system of equations to represent the situation. Identify the variables and constants.

• 5x + 2y = 50; x, y >= 0

• 3x + 4y = 50; x, y >= 0

• 2x + 5y = 50; x, y >= 0

• 10x + y = 50; x, y >= 0

John is saving money for a video game that costs $60. He saves $5 each week from his allowance and $3 each week from doing chores. Write a system of equations to model his savings over time. Graph the equations to find out when he can buy the game.

• John can buy the game after 12 weeks.

• John can buy the game after 6 weeks.

• John can buy the game after 8 weeks.

• John can buy the game after 10 weeks.

A store sells two types of gift cards: one for $25 and another for $50. If a customer buys a total of 5 gift cards and spends $200, write a system of equations to represent the number of each type of gift card purchased. Identify the variables and constants.

• x + y = 6; 25x + 50y = 250

• x + y = 4; 25x + 50y = 150

• x + y = 5; 20x + 50y = 200

• x + y = 5; 25x + 50y = 200

Samantha is saving for a new bicycle that costs $120. She saves $10 each week from her allowance and $5 each week from her part-time job. Write a system of equations to model her savings. Graph the equations to determine how many weeks it will take her to save enough money.

• 10 weeks

• 8 weeks

• 6 weeks

• 12 weeks

A family is planning a vacation and has a budget of $800. They plan to spend $200 on hotel and $100 on food each day. Write a system of equations to represent their spending. Identify the variables and constants, and graph the equations to find out how many days they can afford to stay.

• 1 day

• 3 days

• 2 days

• 4 days

Tom and Jerry are saving money to buy a new video game console. Tom saves $15 a week, while Jerry saves $10 a week. If they want to save a total of $300 together, write a system of equations to represent their savings. Identify the variables and constants.

• 10T + 15J = 300; T = J

• 20T + 5J = 300; T = J - 2

• 15T + 10J = 300; T = J

• 15T + 10J = 250; T = J + 5

A farmer sells apples for $3 each and oranges for $2 each. If he sells a total of 100 fruits and makes $240, write a system of equations to represent the number of apples and oranges sold. Identify the variables and constants, and graph the equations to find the solution.

• Apples: 20, Oranges: 80

• Apples: 50, Oranges: 50

• Apples: 40, Oranges: 60

• Apples: 30, Oranges: 70

Lisa is saving money to buy a new phone that costs $500. She saves $20 each week from her job and $10 each week from her allowance. Write a system of equations to model her savings. Graph the equations to determine how many weeks it will take her to save enough money.

• 15 weeks

• 20 weeks

• 17 weeks

• 10 weeks

A school is selling tickets for a fundraiser. Adult tickets cost $10 and student tickets cost $5. If they sell a total of 150 tickets and make $1000, write a system of equations to represent the number of adult and student tickets sold. Identify the variables and constants.

• 2x + y = 150, 5x + 10y = 1000

• x + y = 100, 10x + 5y = 500

• x + y = 150, 10x + 5y = 1000

• x + 2y = 150, 10x + 2y = 1000

A couple is saving for a wedding that costs $10,000. They save $200 each month from their salaries and $100 each month from side jobs. Write a system of equations to model their savings. Graph the equations to find out how many months it will take them to reach their goal.

• 40 months

• 25 months

• 30 months

• 34 months