Solving Real-World Problems with Systems of Equations

A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If they sold a total of 150 tickets for $1,200, how many adult and student tickets were sold? Write the system of equations and analyze the solution.

• 60 adult tickets and 90 student tickets were sold.

• 100 adult tickets and 50 student tickets were sold.

• 80 adult tickets and 70 student tickets were sold.

• 90 adult tickets and 60 student tickets were sold.

A farmer has two types of fruit trees: apple and orange. He has a total of 80 trees, and the number of apple trees is twice the number of orange trees. Write the equations and find out how many of each type of tree he has.

• Apple trees: 54, Orange trees: 26

• Apple trees: 40, Orange trees: 40

• Apple trees: 30, Orange trees: 50

• Apple trees: 60, Orange trees: 20

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $15 a week, while Jamie saves $10 a week. If Alex has $30 more than Jamie after a certain number of weeks, write the system of equations and determine how many weeks they have been saving.

• 10 weeks

• 8 weeks

• 4 weeks

• 6 weeks

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. If a customer drives 100 miles, which company is cheaper? Write the equations and analyze the solution.

• The first company is cheaper.

• The second company charges a flat fee of $40.

• Both companies charge the same amount.

• The second company is cheaper.

In a school, the number of boys is 10 more than twice the number of girls. If the total number of students is 70, write the system of equations and find the number of boys and girls in the school.

• Number of boys: 30, Number of girls: 40

• Number of boys: 50, Number of girls: 20

• Number of boys: 60, Number of girls: 10

• Number of boys: 40, Number of girls: 30

A bookstore sells novels for $12 each and textbooks for $20 each. If a customer buys a total of 10 books for $150, how many novels and textbooks did they buy? Write the equations and analyze the solution.

• 7 novels and 3 textbooks

• 5 novels and 5 textbooks

• 6 novels and 4 textbooks

• 4 novels and 6 textbooks

A local gym offers two membership plans. Plan A costs $25 per month, and Plan B costs $15 per month plus a one-time fee of $100. After how many months will both plans cost the same? Write the system of equations and find the solution.

• 5 months

• 8 months

• 10 months

• 12 months

A movie theater has two types of seating: regular and VIP. Regular seats cost $8 each, and VIP seats cost $12 each. If a total of 200 seats were sold for $1,800, how many of each type were sold? Write the equations and analyze the solution.

• 100 regular seats and 100 VIP seats were sold.

• 150 regular seats and 50 VIP seats were sold.

• 200 regular seats and 0 VIP seats were sold.

• 80 regular seats and 120 VIP seats were sold.

A pet store has cats and dogs. The number of cats is three times the number of dogs. If there are 40 pets in total, write the system of equations and determine how many cats and dogs are in the store.

• 20 cats and 20 dogs

• 30 cats and 10 dogs

• 35 cats and 5 dogs

• 25 cats and 15 dogs

A bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 50 items for $120, how many cupcakes and cookies did they buy? Write the equations and analyze the solution.

• 25 cupcakes and 25 cookies

• 20 cupcakes and 30 cookies

• 10 cupcakes and 40 cookies

• 15 cupcakes and 35 cookies