Mastering Elimination: Solve & Verify Systems of Equations

A farmer has chickens and cows. If the total number of animals is 30 and the total number of legs is 100, how many chickens and cows does the farmer have? Use the elimination method to solve and check your solution.

• 5 chickens and 25 cows

• 15 chickens and 15 cows

• 10 chickens and 20 cows

• 20 chickens and 10 cows

Two friends, Alex and Jamie, are collecting stickers. Alex has 5 more stickers than Jamie, and together they have 45 stickers. How many stickers does each friend have? Use the elimination method and verify your answer.

• Alex has 30 stickers and Jamie has 15 stickers.

• Alex has 20 stickers and Jamie has 25 stickers.

• Alex has 10 stickers and Jamie has 35 stickers.

• Alex has 25 stickers and Jamie has 20 stickers.

A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If they sold a total of 200 tickets for $1500, how many adult and student tickets were sold? Use elimination to find the solution and check your work.

• 200 adult tickets and 0 student tickets were sold.

• 100 adult tickets and 100 student tickets were sold.

• 50 adult tickets and 150 student tickets were sold.

• 150 adult tickets and 50 student tickets were sold.

In a bookstore, the total number of books is 120. If the number of fiction books is twice the number of non-fiction books, how many fiction and non-fiction books are there? Solve using the elimination method and confirm your solution.

• Fiction books: 50, Non-fiction books: 70

• Fiction books: 100, Non-fiction books: 20

• Fiction books: 60, Non-fiction books: 60

• Fiction books: 80, Non-fiction books: 40

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer paid $70 for their rental, how many miles did they drive? Use the elimination method to find the answer and check your calculations.

• 100 miles

• 120 miles

• 80 miles

• 50 miles

A concert hall has two types of seating: regular and VIP. If the total number of seats is 500 and the VIP seats are 100 more than the regular seats, how many regular and VIP seats are there? Solve using elimination and verify your solution.

• Regular seats: 150, VIP seats: 350

• Regular seats: 200, VIP seats: 300

• Regular seats: 300, VIP seats: 200

• Regular seats: 250, VIP seats: 250

In a fruit market, the total number of apples and oranges is 80. If there are 20 more apples than oranges, how many apples and oranges are there? Use the elimination method to solve and check your answer.

• 60 apples and 20 oranges

• 40 apples and 40 oranges

• 30 apples and 50 oranges

• 50 apples and 30 oranges

A local gym has two types of memberships: basic and premium. If there are 150 members in total and the number of premium members is three times the number of basic members, how many members are in each category? Use elimination to find the solution and confirm your answer.

• 37 basic members and 113 premium members

• 75 basic members and 75 premium members

• 50 basic members and 100 premium members

• 30 basic members and 120 premium members

A bakery sells muffins and cookies. If the total number of baked goods is 200 and the number of muffins is 50 more than the number of cookies, how many muffins and cookies are there? Solve using the elimination method and check your solution.

• 75 cookies and 125 muffins

• 100 cookies and 100 muffins

• 80 cookies and 120 muffins

• 50 cookies and 150 muffins

A movie theater has two types of tickets: adult and child. If the total number of tickets sold is 300 and the number of adult tickets is 50 more than child tickets, how many adult and child tickets were sold? Use the elimination method to solve and verify your answer.

• Adult tickets: 175, Child tickets: 125

• Adult tickets: 200, Child tickets: 100

• Adult tickets: 150, Child tickets: 150

• Adult tickets: 100, Child tickets: 200