Rational Equations in Real Life: Solving and Checking Solutions

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer paid $70, how many miles did they drive? Solve the equation and check for extraneous solutions.

• 200 miles

• 150 miles

• 50 miles

• 100 miles

A recipe requires 3/4 cup of sugar for every 2 cups of flour. If you have 1 cup of sugar, how many cups of flour can you use? Set up the rational equation and solve it, checking for extraneous solutions.

• 4 cups of flour

• 2.67 cups of flour

• 3 cups of flour

• 1.5 cups of flour

A tank can be filled by two pipes. Pipe A can fill the tank in 4 hours, while Pipe B can fill it in 6 hours. If both pipes are opened together, how long will it take to fill the tank? Solve the equation and check for extraneous solutions.

• 1.5 hours

• 2.4 hours

• 3 hours

• 5 hours

A cyclist travels at a speed of 12 miles per hour. If they travel for 1 hour and 30 minutes, how far do they go? Set up a rational equation to find the distance and check for extraneous solutions.

• 20 miles

• 12 miles

• 15 miles

• 18 miles

A store sells pencils for $0.50 each and erasers for $0.75 each. If a student buys a total of 10 items for $6.00, how many of each item did they buy? Create a rational equation and solve it, checking for extraneous solutions.

• 7 pencils and 3 erasers

• 6 pencils and 4 erasers

• 4 pencils and 6 erasers

• 5 pencils and 5 erasers

A swimming pool can be filled by two hoses. Hose A can fill the pool in 5 hours, and Hose B can fill it in 3 hours. If both hoses are used together, how long will it take to fill the pool? Solve the equation and check for extraneous solutions.

• 4.5 hours

• 3.5 hours

• 1.875 hours

• 2 hours

A recipe calls for 2/3 cup of oil for every 1 cup of vinegar. If you want to use 1 cup of vinegar, how much oil do you need? Set up the rational equation and solve it, checking for extraneous solutions.

• 1/2 cup of oil

• 2/3 cup of oil

• 1 cup of oil

• 3/4 cup of oil

A gardener has a rectangular garden that is 10 feet long and 6 feet wide. If they want to increase the area by 50 square feet, what will be the new dimensions? Set up a rational equation and solve it, checking for extraneous solutions.

• New dimensions are approximately 13.54 feet by 8.12 feet.

• New dimensions are 11 feet by 6.5 feet.

• New dimensions are 15 feet by 9 feet.

• New dimensions are 12 feet by 7 feet.

A train travels 60 miles in 1.5 hours. If it continues at the same speed, how far will it travel in 4 hours? Create a rational equation to find the distance and check for extraneous solutions.

• 200 miles

• 120 miles

• 160 miles

• 80 miles

A student scored 80% on a test with 50 questions. If they answered 10 questions incorrectly, how many questions did they answer correctly? Set up a rational equation and solve it, checking for extraneous solutions.

• 30

• 50

• 45

• 40