Real-Life Linear Equations: Word Problems to Formulas

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 the car for m miles.

• C = 0.20m - 30

• 20m - C = 3000

• C = 30m + 0.20

• C = 30 + 0.20m

A school is planning a field trip and has a budget of $500. The cost per student is $25. Write a linear equation in standard form to represent the number of students (s) that can attend the trip within the budget.

• 25s - 500 = 0

• 30s - 500 = 0

• 20s - 500 = 0

• 25s + 500 = 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.

• 2w - l = -3

• l + 3 = 2w

• l = 2w + 3

• l - 2w = 3

A bookstore sells notebooks for $2 each and pens for $1 each. If a student buys a total of 10 items and spends $16, write a linear equation in standard form to represent the number of notebooks (n) and pens (p) bought.

• 2n + p = 16

• n + p = 16

• 3n + 2p = 20

• n + 2p = 10

A concert hall has a seating capacity of 800. If the number of rows is represented by r and each row has 20 seats, write a linear equation in standard form to represent the relationship between the number of rows and total seating capacity.

• 15r - 800 = 0

• 25r - 800 = 0

• 20r + 800 = 0

• 20r - 800 = 0

A factory produces 150 toys per hour. If the factory operates for h hours, write a linear equation in standard form to represent the total number of toys (T) produced.

• 150h - T = 0

• T = 150h - 1

• T = 150h + 0

• T = 150 + h

A taxi company charges a base fare of $5 plus $2 for each mile driven. Write a linear equation in standard form to represent the total fare (F) for a trip of m miles.

• F = 5 + 2m + 3

• 2m - F = -5

• F = 5m + 2

• F = 2m + 5

A local 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 attending c classes in a month.

• 10c - C = -40

• C = 40 + 10c + 20

• C = 10c + 40

• C = 40c - 10

A farmer has a total of 120 acres of land. He wants to plant corn and wheat, with corn taking 2 acres per field and wheat taking 3 acres per field. Write a linear equation in standard form to represent the relationship between the number of corn fields (c) and wheat fields (w).

• 2c + 2w = 120

• 2c + 4w = 120

• 3c + 2w = 120

• 2c + 3w = 120

A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer buys a total of 5 pizzas and spends $52, write a linear equation in standard form to represent the number of small pizzas (s) and large pizzas (l) bought.

• 8s + 12l = 52, s + l = 5

• 6s + 12l = 52, s + l = 4

• 8s + 10l = 52, s + l = 6

• 7s + 10l = 52, s + l = 5