8th Grade Algebra: Solve and Graph Systems of Equations

A local bakery sells cupcakes and cookies. The total number of baked goods is 50. If the number of cupcakes is twice the number of cookies, how many cupcakes and cookies are there? Check your solution for accuracy and graph the equations.

• 30 cupcakes and 20 cookies

• 15 cupcakes and 35 cookies

• 40 cupcakes and 10 cookies

• 25 cupcakes and 25 cookies

A school is organizing a field trip. The cost per student is $30, and the total cost for 20 students is $600. If the school also has to pay a fixed fee of $100, how many students can they take if they want to keep the total cost under $800? Solve the system and graph the equations.

• 25

• 20

• 23

• 30

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $5 a week, while Jamie saves $10 a week. If Alex has $20 saved already and Jamie has $30, how many weeks will it take for them to have the same amount saved? Check your solution and graph the equations.

• They will never have the same amount saved.

• They will have the same amount saved in 2 weeks.

• Alex will catch up to Jamie in 4 weeks.

• Jamie will always save less than Alex.

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Another company charges a flat fee of $30 plus $0.25 per mile. How many miles must you drive for the costs to be the same? Solve the system and graph the equations.

• 200 miles

• 400 miles

• 300 miles

• 500 miles

A farmer has chickens and cows. The total number of animals is 30, and the number of chickens is 5 more than twice the number of cows. How many chickens and cows does the farmer have? Check your solution for accuracy and graph the equations.

• 25 chickens and 10 cows

• 30 chickens and 0 cows

• 10 chickens and 20 cows

• 20 chickens and 15 cows

In a school, the number of boys is 10 more than the number of girls. If the total number of students is 70, how many boys and girls are there? Solve the system and graph the equations to visualize the solution.

• 30 boys and 40 girls

• 35 boys and 35 girls

• 50 boys and 20 girls

• 40 boys and 30 girls

A movie theater sells adult tickets for $12 and child tickets for $8. If they sold a total of 100 tickets and made $960, how many adult and child tickets were sold? Check your solution for accuracy and graph the equations.

• 30 adult tickets and 70 child tickets were sold.

• 40 adult tickets and 60 child tickets were sold.

• 20 adult tickets and 80 child tickets were sold.

• 50 adult tickets and 50 child tickets were sold.

A bookstore sells novels and magazines. The total number of books sold is 120, and the number of novels is 3 times the number of magazines. How many novels and magazines were sold? Solve the system and graph the equations to confirm your answer.

• 80 novels and 40 magazines

• 100 novels and 20 magazines

• 60 novels and 60 magazines

• 90 novels and 30 magazines

A gym offers two membership plans. Plan A costs $30 per month, and Plan B costs $20 per month plus a one-time fee of $60. After how many months will the costs of both plans be equal? Solve the system and graph the equations to find the solution.

• 6 months

• 4 months

• 10 months

• 8 months

A concert hall has two types of seating: regular and VIP. The total number of seats is 200, and the number of VIP seats is 50 less than twice the number of regular seats. How many regular and VIP seats are there? Check your solution for accuracy and graph the equations.

• Regular seats: 80, VIP seats: 120

• Regular seats: 150, VIP seats: 50

• Regular seats: 90, VIP seats: 110

• Regular seats: 100, VIP seats: 100