Translating Real-Life Scenarios into Linear Equations

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write an equation in standard form to represent the total cost (C) of renting a car for x miles. Identify the variables in your equation.

• 20x - C + 3000 = 0

• C = 30x + 0.20

• C = 0.20x - 30

• C = 30 + 0.20x

A gardener is planting flowers in a rectangular garden. The length of the garden is 3 feet longer than twice the width. If the total area of the garden is 120 square feet, write an equation in standard form to represent this situation. Identify the variables in your equation.

• 3w^2 + 2w - 120 = 0

• w^2 + 2w - 120 = 0

• 2w^2 + 3w - 120 = 0

• 2w^2 - 3w - 120 = 0

A bookstore sells novels for $12 each and textbooks for $20 each. If a customer buys a total of 10 books for $180, write an equation in standard form to represent the number of novels (n) and textbooks (t) purchased. Identify the variables in your equation.

• 5n + 25t = 180

• 10n + 15t = 180

• 12n + 15t = 180

• 12n + 20t = 180

A local gym charges a monthly membership fee of $40 plus $5 for each class attended. Write an equation in standard form to represent the total cost (C) for a member who attends x classes in a month. Identify the variables in your equation.

• C = 40 + 5x

• C = 40x + 5

• 5x + C = 40

• C = 5x - 40

A factory produces two types of toys: action figures and dolls. The factory can produce a total of 200 toys in a day. If the number of action figures produced is twice the number of dolls, write an equation in standard form to represent this situation. Identify the variables in your equation.

• 2x + y = 200

• 3x - 2y = 0

• x + 2y = 200

• x - y = 0

A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer orders a total of 5 pizzas for $56, write an equation in standard form to represent the number of small (s) and large (l) pizzas ordered. Identify the variables in your equation.

• 8s + 12l = 56

• 4s + 16l = 56

• 10s + 8l = 56

• 6s + 10l = 56

A farmer has a total of 100 animals, which are either cows or chickens. If there are 3 times as many chickens as cows, write an equation in standard form to represent the number of cows (c) and chickens (h). Identify the variables in your equation.

• c + h = 200 and h + 3c = 0

• c + h = 50 and h = 3c

• c - h = 100 and h = 3c

• c + h = 100 and h - 3c = 0

A concert hall has a seating capacity of 1,200. If the number of VIP seats is 3 times the number of regular seats, write an equation in standard form to represent the number of VIP (v) and regular (r) seats. Identify the variables in your equation.

• 5r + v = 1200

• r + v = 1200

• 4r + v = 1200

• 2r + v = 1200

A company produces two types of gadgets. The production of gadget A requires 2 hours, while gadget B requires 3 hours. If the company has 24 hours available for production, write an equation in standard form to represent the number of gadget A (a) and gadget B (b) produced. Identify the variables in your equation.

• 2a + 4b = 24

• 2a + 3b = 24

• 2a + 2b = 24

• 3a + 2b = 24