8th Grade Quiz: Solving Systems with Substitution & Elimination

A school is planning a field trip. The cost of a bus is $200 and the cost of tickets is $10 each. If the total cost for 5 tickets is $300, how many buses are needed? Use the substitution method to solve.

• 4

• 1

• 3

• 2

Maria and John are saving money for a concert. Maria has $50 and saves $10 each week, while John has $30 and saves $15 each week. How many weeks will it take for them to have the same amount of money? Use the elimination method to find the solution.

• 4 weeks

• 8 weeks

• 6 weeks

• 2 weeks

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 substitution method to solve the problem.

• 15 chickens and 15 cows

• 5 chickens and 25 cows

• 12 chickens and 18 cows

• 10 chickens and 20 cows

Two friends, Alex and Jamie, are collecting stickers. Alex has 3 times as many stickers as Jamie. Together, they have 48 stickers. How many stickers does each friend have? Use the elimination method to find the answer.

• Alex has 24 stickers and Jamie has 24 stickers.

• Alex has 30 stickers and Jamie has 18 stickers.

• Alex has 40 stickers and Jamie has 8 stickers.

• Alex has 36 stickers and Jamie has 12 stickers.

A bookstore sells novels for $12 each and magazines for $5 each. If a customer buys a total of 10 items and spends $80, how many novels and magazines did they buy? Use the substitution method to solve this problem.

• 4 novels and 6 magazines

• 6 novels and 4 magazines

• 3 novels and 7 magazines

• 5 novels and 5 magazines

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? Use the elimination method to find the solution.

• 12 boys and 13 girls

• 20 boys and 5 girls

• 10 boys and 15 girls

• 15 boys and 10 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? Use the substitution method to solve the problem.

• 150 miles

• 100 miles

• 200 miles

• 50 miles

A local gym offers two membership plans. Plan A costs $30 per month, and Plan B costs $20 per month plus a one-time fee of $60. If a customer wants to spend the same amount on both plans after 6 months, how much would they spend? Use the elimination method to find the answer.

• $120

• $240

• $150

• $180

A concert hall has two types of tickets: regular tickets for $25 and VIP tickets for $50. If a total of 100 tickets were sold for $3,000, how many of each type of ticket were sold? Use the substitution method to solve this problem.

• 80 regular tickets and 20 VIP tickets

• 90 regular tickets and 10 VIP tickets

• 60 regular tickets and 40 VIP tickets

• 70 regular tickets and 30 VIP tickets

In a fruit market, apples cost $2 each and bananas cost $1 each. If a customer buys a total of 20 fruits and spends $30, how many apples and bananas did they buy? Use the elimination method to find the solution.

• 15 apples and 5 bananas

• 5 apples and 15 bananas

• 10 apples and 10 bananas

• 12 apples and 8 bananas