Grade 9 Matrix Word Problems: Substitution & Elimination

A school is organizing a trip for two classes. Class A has 30 students and Class B has 20 students. If the total cost of the trip is $600, and Class A pays $20 per student while Class B pays $15 per student, how much does each class contribute? Use the substitution method to solve.

• Class A contributes $500 and Class B contributes $100.

• Class A contributes $250 and Class B contributes $350.

• Class A contributes $300 and Class B contributes $300.

• Class A contributes $400 and Class B contributes $200.

A farmer has two types of crops: corn and wheat. He has a total of 100 acres to plant. If he plants 3 acres of corn for every 2 acres of wheat, how many acres of each crop does he plant? Use the elimination method to find the solution.

• 50 acres of corn and 50 acres of wheat

• 60 acres of corn and 40 acres of wheat

• 80 acres of corn and 20 acres of wheat

• 70 acres of corn and 30 acres of wheat

A bookstore sells two types of books: fiction and non-fiction. The fiction books cost $12 each and the non-fiction books cost $15 each. If a customer buys a total of 10 books for $135, how many of each type did they buy? Use the substitution method to solve.

• 4 fiction books and 6 non-fiction books

• 6 fiction books and 4 non-fiction books

• 5 fiction books and 5 non-fiction books

• 3 fiction books and 7 non-fiction books

In a concert, tickets for adults cost $25 and tickets for children cost $15. If 200 tickets were sold for a total of $4000, how many adult and child tickets were sold? Use the elimination method to find the answer.

• 100 adult tickets and 100 child tickets

• 150 adult tickets and 50 child tickets

• 200 adult tickets and 0 child tickets

• 50 adult tickets and 150 child tickets

A company produces two products, A and B. Product A requires 2 hours of labor and Product B requires 3 hours. If the company has 60 hours of labor available and produces a total of 20 products, how many of each product does it produce? Use the substitution method to solve.

• Product A: 10, Product B: 10

• Product A: 20, Product B: 0

• Product A: 5, Product B: 15

• Product A: 0, Product B: 20

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month and the premium costs $50 per month. If a total of 50 memberships were sold for $1800, how many of each type were sold? Use the elimination method to find the solution.

• 35 basic memberships and 15 premium memberships were sold.

• 40 basic memberships and 10 premium memberships were sold.

• 30 basic memberships and 20 premium memberships were sold.

• 25 basic memberships and 25 premium memberships were sold.

A delivery service has two types of packages: small and large. A small package costs $5 to deliver and a large package costs $10. If the total delivery cost for 30 packages is $200, how many small and large packages were delivered? Use the substitution method to solve.

• 10 small packages and 20 large packages

• 25 small packages and 5 large packages

• 15 small packages and 15 large packages

• 20 small packages and 10 large packages

A local bakery sells two types of pastries: muffins and croissants. Muffins are sold for $2 each and croissants for $3 each. If the bakery sold a total of 50 pastries for $120, how many muffins and croissants were sold? Use the elimination method to find the answer.

• 25 muffins and 25 croissants

• 20 muffins and 30 croissants

• 30 muffins and 20 croissants

• 40 muffins and 10 croissants

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 $1000, how many adult and student tickets were sold? Use the substitution method to solve.

• 50 adult tickets and 100 student tickets were sold.

• 60 adult tickets and 90 student tickets were sold.

• 70 adult tickets and 80 student tickets were sold.

• 30 adult tickets and 120 student tickets were sold.

A car rental company has two types of cars: economy and luxury. The economy cars rent for $30 per day and the luxury cars for $60 per day. If they rented a total of 40 cars for $1800, how many of each type were rented? Use the elimination method to find the solution.

• 30 economy cars and 10 luxury cars were rented.

• 20 economy cars and 20 luxury cars were rented.

• 25 economy cars and 15 luxury cars were rented.

• 10 economy cars and 30 luxury cars were rented.