Solving & Graphing: Substitution Method Challenges for 8th Grade

A farmer has chickens and cows. If the total number of animals is 30 and the number of chickens is twice the number of cows, how many chickens and cows does the farmer have? Check for extraneous solutions and graph the number of cows on a number line.

• Cows: 20, Chickens: 10

• Cows: 10, Chickens: 20

• Cows: 15, Chickens: 15

• Cows: 5, Chickens: 25

A school is planning a field trip. The cost per student is $15, and the total cost for 20 students is $300. If the school wants to add 5 more students, how much will the total cost change? Use substitution to find the new total and graph the change on a number line.

• $75

• $150

• $100

• $50

A recipe requires 2 cups of flour and 3 cups of sugar. If you want to make a half batch, how much of each ingredient do you need? Use substitution to find the amounts and graph the flour needed on a number line.

• 2 cups of flour and 2 cups of sugar.

• 1.5 cups of flour and 2 cups of sugar.

• 2 cups of flour and 1 cup of sugar.

• 1 cup of flour and 1.5 cups of sugar.

In a class, the ratio of boys to girls is 4:5. If there are 36 students in total, how many boys and girls are there? Use substitution to find the numbers and check for extraneous solutions. Graph the number of boys on a number line.

• 14 boys and 22 girls

• 18 boys and 18 girls

• There are 16 boys and 20 girls.

• 20 boys and 16 girls

A car rental company charges a flat fee of $20 plus $0.50 per mile driven. If a customer paid $45, how many miles did they drive? Use substitution to find the miles and graph the solution on a number line.

• 60 miles

• 30 miles

• 40 miles

• 50 miles

A bookstore sells novels for $10 each and magazines for $5 each. If a customer buys a total of 8 items for $50, how many novels and magazines did they buy? Use substitution to find the quantities and check for extraneous solutions.

• 1 novel and 7 magazines

• 3 novels and 5 magazines

• 2 novels and 6 magazines

• 4 novels and 4 magazines

A swimming pool can be filled by two hoses. Hose A can fill the pool in 4 hours, while Hose B can fill it in 6 hours. If both hoses are used together, how long will it take to fill the pool? Use substitution to find the time and graph the solution on a number line.

• 3 hours

• 5 hours

• 2.4 hours

• 1.5 hours

A concert hall has 200 seats. If 60% of the seats are filled, how many seats are empty? Use substitution to find the number of empty seats and graph the solution on a number line.

• 80

• 60

• 100

• 120

A store sells pencils for $0.50 each and erasers for $1.00 each. If a student buys a total of 10 items for $7.00, how many pencils and erasers did they buy? Use substitution to find the quantities and check for extraneous solutions.

• 5 pencils and 5 erasers

• 7 pencils and 3 erasers

• 6 pencils and 4 erasers

• 4 pencils and 6 erasers