Solving Real-World Math Problems: No Solutions & Expressions

A bakery sells cupcakes for $2 each and cookies for $1 each. If a customer buys a total of 10 items for $15, how many cupcakes and cookies did they buy? Determine if there is no solution, one solution, or infinite solutions.

• 5 cupcakes and 5 cookies

• 10 cookies and 0 cupcakes

• 6 cupcakes and 4 cookies

• 3 cupcakes and 7 cookies

A school is planning a field trip. They have 30 students and need to arrange buses that hold 10 students each. If they can only use whole buses, how many buses are needed? Is there one solution, no solution, or infinite solutions?

• 3 buses are needed.

• 5 buses are needed.

• 4 buses are needed.

• 2 buses are needed.

Two friends, Alex and Jamie, are saving money. Alex saves $5 a week, while Jamie saves $10 a week. If they both start with $20, will they ever have the same amount of money? Explain if there is one solution, no solution, or infinite solutions.

• They will have the same amount of money only at the start.

• They will have the same amount of money after 5 weeks.

• They will never have the same amount of money again.

• They will always have the same amount of money.

A gardener is planting flowers in rows. If each row has the same number of flowers and there are 24 flowers total, how many flowers can be in each row? Can you find one solution, no solution, or infinite solutions?

• 10

• 1, 2, 3, 4, 6, 8, 12, 24

• 15

• 5

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer pays $70, how many miles did they drive? Is there one solution, no solution, or infinite solutions?

• 150 miles

• 100 miles

• 200 miles

• 50 miles

A store sells pencils for $0.50 each and erasers for $1.00 each. If a student buys 12 items for $8, how many pencils and erasers did they buy? Determine if there is no solution, one solution, or infinite solutions.

• 8 pencils and 4 erasers

• 6 pencils and 6 erasers

• 4 pencils and 8 erasers

• 10 pencils and 2 erasers

Two equations are given: 2x + 3y = 12 and 4x + 6y = 24. Are these equations independent, dependent, or inconsistent? Explain your reasoning.

• Inconsistent

• Independent

• Dependent

• Non-linear

A recipe requires 2 cups of flour and 3 cups of sugar. If you have 6 cups of flour, how many cups of sugar can you use while maintaining the same ratio? Is there one solution, no solution, or infinite solutions?

• 9 cups of sugar

• 4 cups of sugar

• 12 cups of sugar

• 6 cups of sugar

A concert hall has 200 seats. If tickets are sold for $20 each and the total revenue is $3,000, how many tickets were sold? Determine if there is one solution, no solution, or infinite solutions.

• 75

• 100

• 200

• 150