Exploring Rational Functions: Real-Life Applications for 9th Graders

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a rational function to represent the total cost, C, as a function of miles driven, m. Simplify the expression for C.

• C(m) = 50 - 0.20m

• C(m) = 50 + 0.50m

• C(m) = 0.20m - 50

• C(m) = 50 + 0.20m

A recipe requires 3/4 cup of sugar for every 2 cups of flour. If you want to make a batch with 6 cups of flour, how much sugar will you need? Write a rational function and simplify it.

• 6 cups of sugar

• 9/4 cups of sugar

• 3 cups of sugar

• 1 cup of sugar

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. Write a rational function to represent the rate at which the tank fills when both pipes are open. Simplify your answer.

• 5/12

• 3/8

• 2/3

• 1/2

A school is planning a field trip and has a budget of $300. If the cost per student is represented by the rational function C = 300/n, where n is the number of students, how much can each student pay if 15 students attend?

• 25

• 20

• 30

• 15

A farmer has a rectangular field with a length that is 3 meters longer than its width. If the area of the field is 54 square meters, write a rational function to express the width in terms of the length and simplify it.

• w = (54 / L) - 3

• w = (54 / L) + 3

• w = L - 54

• w = 54 / (L - 3)

A swimming pool is being filled at a rate of 5 gallons per minute. If the pool holds 1,200 gallons, write a rational function to represent the time, t, in minutes, to fill the pool. Simplify the expression for t.

• t = 150 minutes

• t = 180 minutes

• t = 300 minutes

• t = 240 minutes

A store sells a product for $80, but offers a discount of 20% for members. Write a rational function to represent the final price, P, as a function of the original price, O. Simplify your expression for P.

• P = O + 20%

• P = 0.80 * O

• P = 0.60 * O

• P = O - 0.20 * O

A cyclist travels at a speed of 12 miles per hour. If the cyclist takes a break every 30 minutes, write a rational function to represent the total distance traveled, D, as a function of time, t, in hours. Simplify your expression for D.

• D(t) = 12t + 3(t // 0.5)

• D(t) = 12t + 6(t // 0.5)

• D(t) = 12t - 12(t // 1)

• D(t) = 12t - 6(t // 0.5)

A recipe calls for 2/3 cup of oil for every 1/2 cup of vinegar. If you want to make a larger batch using 3 cups of vinegar, write a rational function to express the amount of oil needed and simplify it.

• 4 cups of oil

• 5 cups of oil

• 2 cups of oil

• 3 cups of oil

A delivery truck can carry a maximum weight of 1,500 pounds. If each package weighs 30 pounds, write a rational function to determine the maximum number of packages, n, that can be delivered. Simplify your expression for n.

• 50

• 40

• 60

• 70