Writing Linear Equations from Real-Life Word Problems

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

• C = 30 + 0.20x

• C = 0.20x - 30

• C = 30x + 0.20

• 20x - C + 3000 = 0

Maria is saving money to buy a new bike. She has $50 saved and plans to save an additional $15 each week. Write a linear equation in standard form to represent the total amount of money (M) she will have after w weeks.

• M = 50 - 15w

• 15w - M = -50

• 15w + M = 50

• M = 15w + 50

A school is planning a field trip and needs to rent a bus. The bus rental costs $200 plus $5 per student. Write a linear equation in standard form to represent the total cost (T) of the trip for s students.

• T + 5s = 200

• T = 200 - 5s

• 5s + T = 200

• 5s - T = -200

John is buying apples and oranges. Apples cost $2 each and oranges cost $3 each. If he buys a total of 10 fruits for $24, write a linear equation in standard form to represent the relationship between the number of apples (a) and oranges (o).

• a + o = 10 and 2a + 3o = 24

• a + o = 8 and 2a + 3o = 30

• a + o = 10 and 2a + 3o = 18

• a + o = 12 and 2a + 3o = 20

A gym charges a monthly membership fee of $40 plus $10 for each class attended. Write a linear equation in standard form to represent the total cost (C) for m months and c classes attended.

• 50m + 5c - C = 0

• 30m + 15c - C = 0

• 40m + 10c - C = 0

• 40m + 20c - C = 0

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

• W = (L - 3)/2

• L + 3 = 2W

• L = 2W + 3

• 2W - L = -3

A bookstore sells notebooks for $5 each and pens for $2 each. If a student buys a total of 12 items for $40, write a linear equation in standard form to represent the relationship between the number of notebooks (n) and pens (p).

• 6n + p = 12

• 5n + 2p = 40 and n + p = 12

• n + 3p = 40

• 3n + 4p = 40

A factory produces toys and games. The total production cost is $500 plus $15 for each toy produced. Write a linear equation in standard form to represent the total cost (C) for producing t toys.

• C = 15t + 500

• C = 15t + 15

• C = 500 - 15t

• 15t - C = -500

A concert hall has a seating capacity of 500. If tickets are sold for $20 each and the total revenue is $8,000, write a linear equation in standard form to represent the relationship between the number of tickets sold (x) and the total revenue (R).

• 15x + R = 1000

• 25x - R = 500

• 10x - R = 0

• 20x - R = 0

A farmer has a total of 100 animals consisting of cows and chickens. If cows are counted as 2 animals and chickens as 1 animal, write a linear equation in standard form to represent the relationship between the number of cows (c) and chickens (h).

• 3c + h = 100

• 2c + 2h = 100

• 2c + h = 100

• c + h = 100