Solving Real-Life Linear Equations: Check & Interpret

A store sells pencils for $0.50 each and erasers for $0.75 each. If a student buys a total of 10 items and spends $6.00, how many pencils and erasers did they buy? Check your solution for accuracy and interpret the results in context.

• 6 pencils and 4 erasers

• 5 pencils and 5 erasers

• 4 pencils and 6 erasers

• 7 pencils and 3 erasers

Two friends, Alex and Jamie, are saving money for a concert. Alex has $20 and saves $5 each week, while Jamie has $15 and saves $7 each week. After how many weeks will they have the same amount of money? Verify your solution and explain what it means in this scenario.

• 5 weeks

• 2 weeks

• 4 weeks

• 3 weeks

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges $25 plus $0.25 per mile. For what distance will both companies charge the same amount? Solve the equation and interpret the solution in a real-world context.

• 75 miles

• 50 miles

• 100 miles

• 120 miles

A gardener is planting flowers in two different sections of a garden. Section A has 3 times as many flowers as Section B. If the total number of flowers is 48, how many flowers are in each section? Solve the equation and interpret the results in context.

• Section A has 40 flowers and Section B has 8 flowers.

• Section A has 30 flowers and Section B has 18 flowers.

• Section A has 24 flowers and Section B has 24 flowers.

• Section A has 36 flowers and Section B has 12 flowers.

A book costs $12 and a magazine costs $5. If a student buys a total of 8 items and spends $66, how many books and magazines did they buy? Check your solution for accuracy and explain the significance of your findings.

• 2 books and 6 magazines

• 3 books and 5 magazines

• 1 book and 7 magazines

• 4 books and 4 magazines

In a school, the number of boys is 4 more than twice the number of girls. If the total number of students is 28, how many boys and girls are there? Solve the equation and interpret the results in the context of the school population.

• 18 boys and 10 girls

• 16 boys and 12 girls

• 22 boys and 6 girls

• 20 boys and 8 girls

A recipe requires 2 cups of flour and 3 cups of sugar. If you want to make a batch that uses 12 cups of flour, how many cups of sugar will you need? Set up the equation, solve it, and explain the relationship between the ingredients in context.

• 18 cups of sugar

• 12 cups of sugar

• 15 cups of sugar

• 10 cups of sugar

A train travels 60 miles per hour and a car travels 80 miles per hour. If they both leave the same station at the same time, how long will it take for the car to be 30 miles ahead of the train? Solve the equation and interpret the results in a real-world context.

• 2 hours

• 1 hour

• 1.5 hours

• 45 minutes