Standard Form Challenges in Linear Equations for 8th Grade

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 local bakery sells cupcakes for $3 each and cookies for $2 each. If a customer spends $30, write the equation in standard form to represent the relationship between the number of cupcakes (c) and cookies (k) bought.

• 5c + 2k = 30

• 4c + k = 30

• 2c + 3k = 30

• 3c + 2k = 30

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

• 20s - 500 = 0

• 25s - 500 = 0

• 25s + 500 = 0

• 30s - 500 = 0

A gardener is planting flowers in a rectangular garden. The length of the garden is twice the width. If the total area is 200 square feet, write the equation in standard form to represent the relationship between length (l) and width (w).

• l + w = 100

• l^2 - 200 = 0

• 2w^2 - 200 = 0

• w^2 - 100 = 0

A phone plan charges a monthly fee of $30 plus $0.10 per text message sent. Write the equation in standard form that represents the total monthly cost (C) in terms of the number of text messages (t) sent.

• 10t - C = -3000

• C = 30 + 0.10t

• C = 30t + 10

• C = 10t + 300

A bookstore sells novels for $15 each and magazines for $5 each. If a customer buys a total of 10 items and spends $100, write the equation in standard form to represent the relationship between the number of novels (n) and magazines (m) purchased.

• 2n + m = 15

• n + 2m = 30

• 3n + m = 20

• 4n + m = 25

A factory produces toys and games. The total production cost is $2000, with toys costing $10 each and games costing $20 each. Write the equation in standard form to represent the relationship between the number of toys (t) and games (g) produced.

• t + g = 100

• t + 3g = 150

• t + 2g = 200

• 2t + g = 200

A concert venue has a seating capacity of 500. If tickets are sold for $20 each and VIP tickets for $50 each, write the equation in standard form to represent the total revenue (R) in terms of the number of regular tickets (x) and VIP tickets (y) sold.

• 15x + 40y = R

• 30x + 50y = R

• 25x + 45y = R

• 20x + 50y = R

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 the equation in standard form to represent the relationship between the number of cows (c) and chickens (h).

• 2c + h = 100

• c + h = 100

• 3c + h = 100

• 2c + 2h = 100

A company produces two types of products: A and B. Product A costs $30 to produce and product B costs $20. If the total production cost is $600, write the equation in standard form to represent the relationship between the number of products A (a) and B (b) produced.

• 2a + 3b = 60

• 4a + b = 30

• 5a + 2b = 100

• 3a + 2b = 60