Solving and Graphing Systems of Equations in Real-Life Scenarios

A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If they sold a total of 50 tickets for $400, set up a system of equations to represent the situation and find how many adult and student tickets were sold.

• 20 adult tickets and 30 student tickets were sold.

• 25 adult tickets and 25 student tickets were sold.

• 40 adult tickets and 10 student tickets were sold.

• 30 adult tickets and 20 student tickets were sold.

A farmer has chickens and cows. If there are 20 animals in total and they have 60 legs, set up a system of equations to find out how many chickens and cows there are. Graph the equations and check your solution for accuracy.

• 12 chickens and 8 cows

• 5 chickens and 15 cows

• 10 chickens and 10 cows

• 15 chickens and 5 cows

Two friends are saving money for a concert. One saves $15 a week and the other saves $10 a week. If they want to save a total of $150 together, set up a system of equations to find out how many weeks they need to save. Graph the equations and verify your solution.

• 6 weeks

• 4 weeks

• 10 weeks

• 8 weeks

A store sells pencils for $2 each and erasers for $3 each. If a customer buys a total of 10 items for $24, set up a system of equations to determine how many pencils and erasers were purchased. Check your solution by substituting back into the equations.

• 4 pencils and 6 erasers

• 6 pencils and 4 erasers

• 5 pencils and 5 erasers

• 7 pencils and 3 erasers

In a class, the ratio of boys to girls is 3:2. If there are 25 students in total, set up a system of equations to find the number of boys and girls. Graph the equations and check your solution for accuracy.

• There are 15 boys and 10 girls.

• 10 boys and 15 girls.

• 20 boys and 5 girls.

• 12 boys and 13 girls.

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer paid $50 for a rental, set up a system of equations to find out how many miles they drove. Graph the equations and verify your solution.

• 120 miles

• 100 miles

• 80 miles

• 150 miles

A bakery sells muffins for $1.50 each and cookies for $2.00 each. If a customer buys a total of 12 items for $20, set up a system of equations to find out how many muffins and cookies were bought. Check your solution for accuracy.

• 6 muffins and 6 cookies

• 5 muffins and 7 cookies

• 8 muffins and 4 cookies

• 10 muffins and 2 cookies

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 $50. If a customer pays $100, set up a system of equations to find out how many months they signed up for each plan. Graph the equations and check your solution.

• Plan A: 2 months, Plan B: 0 months.

• Plan A: 3 months, Plan B: 1 month.

• Plan A: 0 months, Plan B: 4 months.

• Plan A: 1 month, Plan B: 3 months.

A bookstore sells novels for $12 each and textbooks for $20 each. If a customer buys a total of 8 books for $136, set up a system of equations to determine how many novels and textbooks were purchased. Graph the equations and verify your solution.

• 5 novels and 3 textbooks

• 3 novels and 5 textbooks

• 2 novels and 6 textbooks

• 4 novels and 4 textbooks

A gardener is planting flowers and shrubs. If the total number of plants is 30 and the total cost is $150, with flowers costing $3 each and shrubs costing $5 each, set up a system of equations to find out how many flowers and shrubs were planted. Check your solution for accuracy.

• 15 flowers and 15 shrubs

• 5 flowers and 25 shrubs

• 0 flowers and 30 shrubs

• 10 flowers and 20 shrubs