Mastering Standard Form: Real-Life Linear Equations

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the equation in standard form that represents the total cost (C) in terms of miles driven (m).

• C = 50 + 0.20m

• C = 0.20m - 50

• C = 50m + 0.20

• 0.20m - C = -50

A gardener is planting flowers in a rectangular garden. The length of the garden is 3 feet longer than twice the width. Write the equation in standard form to represent the relationship between the length (l) and width (w) of the garden.

• l + 3 = 2w

• l - 2w = 3

• 2w - l + 3 = 0

• l = 2w + 3

A bookstore sells novels for $12 each and textbooks for $25 each. If a customer spends a total of $200, write the equation in standard form to represent the number of novels (n) and textbooks (t) purchased.

• 15n + 20t = 200

• 10n + 30t = 200

• 12n + 25t = 200

• 20n + 15t = 200

A local gym charges a monthly membership fee of $40 plus $5 for each class attended. Write the equation in standard form that represents the total cost (C) in terms of the number of classes (c) attended.

• C = 40 + 5c

• C = 5c + 40

• 5c - C = -40

• C = 40 - 5c

A factory produces two types of toys: action figures and dolls. The factory produces a total of 500 toys in a day. If the number of action figures produced is twice the number of dolls, write the equation in standard form to represent the relationship between action figures (a) and dolls (d).

• 2d - a = 500

• a + d = 500

• a - 2d = 0

• 3d - a = 0

A farmer has a total of 120 animals, consisting of cows and chickens. If there are 3 times as many chickens as cows, write the equation in standard form to represent the relationship between cows (c) and chickens (h).

• c + h = 100

• c + h = 120, h - 3c = 0

• h = 3c + 20

• c - h = 120

A concert hall has a seating capacity of 800. If the number of VIP seats is 200 and the rest are general admission seats, write the equation in standard form to represent the relationship between VIP seats (v) and general admission seats (g).

• v - g = 200

• v + g = 800

• v + g = 1000

• v + g = 600

A company produces two types of gadgets. The total production is 1,000 gadgets, and the number of type A gadgets is 300 more than type B gadgets. Write the equation in standard form to represent the relationship between type A gadgets (a) and type B gadgets (b).

• a + b = 1000, a - b = 400

• a + b = 800, a - b = 200

• a + b = 1200, a - b = 100

• a + b = 1000, a - b = 300

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A recipe requires 2 cups of flour for every 3 cups of sugar. If you want to make a larger batch using a total of 20 cups of ingredients, write the equation in standard form to represent the relationship between cups of flour (f) and cups of sugar (s).

• 4f - 3s = 5

• 3f - 2s = 0

• 2f + 3s = 20

• f + s = 10