Exploring Real-Life Applications of Polynomials and Equations

A farmer has a rectangular field where the length is represented by p and the width is represented by q. If the area of the field can be expressed as p(qx + r) = 1200 square meters, and the width is 20 meters, what is the length of the field?

• 100 meters

• 40 meters

• 60 meters

• 80 meters

A car rental company charges a base fee of p dollars plus q dollars for each mile driven. If the total cost can be expressed as p(qx + r) = 150, and the base fee is $50, how many miles were driven if the total cost is $150?

• 3 miles

• 2 miles

• 5 miles

• 10 miles

A school is planning a field trip and has a budget represented by p. If the cost per student is q and there are r students, the total cost can be expressed as p(qx + r) = 500. If the cost per student is $10, how many students can attend if the budget is $500?

• 50

• 40

• 60

• 70

A company produces x units of a product, and the profit can be modeled by the equation p(qx + r) = 3000. If the profit per unit is $15 and fixed costs are $300, how many units must be sold to reach a profit of $3000?

• 180

• 220

• 250

• 300

A recipe requires p cups of flour, and if each batch uses q cups plus r additional cups, the total flour used can be expressed as p(qx + r) = 10. If each batch uses 2 cups and 1 additional cup, how many batches can be made?

• 0

• 3

• 5

• 1

A concert venue has a seating capacity represented by p. If the number of tickets sold can be expressed as p(qx + r) = 500, and the venue has 200 seats, how many tickets were sold if the total capacity is reached?

• 500

• 400

• 300

• 200

A gym charges a monthly fee of p dollars plus q dollars for each class attended. If the total cost can be expressed as p(qx + r) = 100, and the monthly fee is $30, how many classes were attended if the total cost is $100?

• 10

• 1

• 3

• 5

A painter charges p dollars for materials and q dollars per hour of work. If the total cost can be expressed as p(qx + r) = 400, and the materials cost $100, how many hours did the painter work if the total cost is $400?

• 100/q hours

• 200/q hours

• 300/q hours (where q is the hourly rate in dollars)

• 400/q hours

A delivery service charges a flat fee of p dollars plus q dollars per mile. If the total cost can be expressed as p(qx + r) = 80, and the flat fee is $20, how many miles were driven if the total cost is $80?

• 2

• 6

• 4

• 8

A bookstore sells p books at a price of q dollars each. If the total revenue can be expressed as p(qx + r) = 200, and each book costs $10, how many books were sold to reach a revenue of $200?

• 25

• 15

• 30

• 20