Solving Systems of Equations: Substitution & Elimination

1. A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If the school sold a total of 150 tickets for $1,200, how many adult and student tickets were sold? Use the substitution method to solve.

• 60 adult tickets and 90 student tickets

• 100 adult tickets and 50 student tickets

• 80 adult tickets and 70 student tickets

• 90 adult tickets and 60 student tickets

2. A farmer has chickens and cows. The total number of animals is 50, and the total number of legs is 140. How many chickens and cows does the farmer have? Apply the elimination method to find the solution.

• 15 chickens and 35 cows

• 30 chickens and 20 cows

• 40 chickens and 10 cows

• 25 chickens and 25 cows

3. Two friends, Alex and Jamie, are saving money for a concert. Alex has $20 more than Jamie, and together they have $120. How much money does each friend have? Use the substitution method to solve the problem.

• Alex has $50, Jamie has $30.

• Alex has $80, Jamie has $60.

• Alex has $60, Jamie has $40.

• Alex has $70, Jamie has $50.

4. A store sells pencils for $0.50 each and erasers for $1.00 each. If a student buys a total of 30 items and spends $20, how many pencils and erasers did the student buy? Apply the elimination method to find the answer.

• 15 pencils and 15 erasers

• 20 pencils and 10 erasers

• 10 pencils and 20 erasers

• 25 pencils and 5 erasers

5. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer paid $50 for a rental, how many miles did they drive? Use the substitution method to solve the equation.

• 80 miles

• 120 miles

• 100 miles

• 60 miles

6. In a class, the ratio of boys to girls is 3:2. If there are 25 students in total, how many boys and girls are there? Apply the elimination method to find the solution.

• 12 boys and 13 girls

• 15 boys and 10 girls

• 20 boys and 5 girls

• 10 boys and 15 girls

7. A bakery sells muffins for $2 each and cookies for $1.50 each. If a customer buys a total of 40 items and spends $70, how many muffins and cookies did they buy? Use the substitution method to solve the problem.

• 15 muffins and 25 cookies

• 30 cookies and 10 muffins

• 20 muffins and 20 cookies

• 25 muffins and 15 cookies

8. A local gym offers two membership plans. Plan A costs $50 per month, and Plan B costs $30 per month plus a one-time fee of $120. If a member pays $240 in total, which plan did they choose? Apply the elimination method to find the answer.

• Plan B

• Plan A

• Plan A with a one-time fee of $120

• Plan B with a monthly fee of $50

9. A movie theater has two types of tickets: regular tickets for $12 and VIP tickets for $20. If a total of 100 tickets were sold for $1,400, how many of each type were sold? Use the substitution method to solve the problem.

• 60 regular tickets and 40 VIP tickets

• 75 regular tickets and 25 VIP tickets

• 70 regular tickets and 30 VIP tickets

• 80 regular tickets and 20 VIP tickets

10. A gardener is planting flowers and shrubs. The total number of plants is 60, and the total cost is $240, with flowers costing $3 each and shrubs costing $5 each. How many flowers and shrubs did the gardener plant? Apply the elimination method to find the solution.

• 30 flowers and 30 shrubs

• 20 flowers and 40 shrubs

• 40 flowers and 20 shrubs

• 10 flowers and 50 shrubs