Solving and Verifying Systems of Equations for 8th Graders

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, how many of each type of ticket did they sell? Check your solution by substituting back into the equations.

• 35 adult tickets and 15 student tickets

• 25 adult tickets and 25 student tickets

• 40 adult tickets and 10 student tickets

• 30 adult tickets and 20 student tickets

Maria and John are saving money for a concert. Maria has $20 more than John. Together, they have $120. How much money does each person have? Verify your answer by checking the total amount.

• John has $40 and Maria has $60.

• John has $50 and Maria has $70.

• John has $30 and Maria has $90.

• John has $60 and Maria has $80.

A farmer has chickens and cows. The total number of animals is 30, and there are 80 legs in total. How many chickens and cows does the farmer have? Confirm your solution by calculating the total number of legs.

• 10 chickens and 20 cows

• 20 chickens and 10 cows

• 25 chickens and 5 cows

• 15 chickens and 15 cows

Two friends, Alex and Jamie, are collecting stickers. Alex has 5 more stickers than Jamie. Together, they have 45 stickers. How many stickers does each friend have? Check your solution by adding their stickers together.

• Alex has 30 stickers and Jamie has 15 stickers.

• Alex has 10 stickers and Jamie has 35 stickers.

• Alex has 20 stickers and Jamie has 25 stickers.

• Alex has 25 stickers and Jamie has 20 stickers.

A bookstore sells fiction and non-fiction books. The fiction books cost $8 each, and the non-fiction books cost $12 each. If 20 books were sold for a total of $180, how many of each type were sold? Verify your answer by substituting back into the equations.

• 12 fiction books and 8 non-fiction books were sold.

• 10 fiction books and 10 non-fiction books were sold.

• 5 fiction books and 15 non-fiction books were sold.

• 15 fiction books and 5 non-fiction books were sold.

In a class, the number of boys is twice the number of girls. If there are 36 students in total, how many boys and girls are there? Check your solution by adding the number of boys and girls together.

• 20 boys and 16 girls

• There are 24 boys and 12 girls.

• 30 boys and 6 girls

• 18 boys and 18 girls

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? Verify your answer by checking the total cost.

• 100 miles

• 50 miles

• 200 miles

• 150 miles

Two types of fruit are being sold at a market: apples and oranges. Apples cost $2 each, and oranges cost $3 each. If a customer buys 10 pieces of fruit for $24, how many apples and oranges did they buy? Confirm your solution by calculating the total cost.

• 6 apples and 4 oranges

• 7 apples and 3 oranges

• 4 apples and 6 oranges

• 5 apples and 5 oranges

A gym has two types of memberships: monthly and yearly. The monthly membership costs $30, and the yearly membership costs $300. If 50 memberships were sold for a total of $1,500, how many of each type were sold? Check your solution by substituting back into the equations.

• 30 monthly memberships and 20 yearly memberships were sold.

• 25 monthly memberships and 25 yearly memberships were sold.

• 0 monthly memberships and 50 yearly memberships were sold.

• 50 monthly memberships and 0 yearly memberships were sold.

A local bakery sells muffins and cookies. Muffins cost $2 each, and cookies cost $1 each. If they sold a total of 100 items for $150, how many muffins and cookies did they sell? Verify your answer by checking the total sales.

• 40 muffins and 60 cookies

• 60 muffins and 40 cookies

• 30 muffins and 70 cookies

• 50 muffins and 50 cookies