Create and Identify Standard Form Equations: Grade 8 Math

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

• 0.20m - C = -50

• C = 50m + 0.20

A school is planning a field trip and has a budget of $300. If each student pays $15, how many students can attend? Write the equation in standard form to represent the relationship between the number of students (s) and the total cost (C).

• 20

• 30

• 25

• 15

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

• 2W - L + 3 = 0

• L = 2W + 3

• L + 3 = 2W

• W = L - 3

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

• n + p = 10, 3n + p = 16

• n + p = 12, 2n + p = 14

• n + p = 8, 2n + p = 18

• n + p = 10, 2n + p = 16

A taxi company charges a base fare of $3 plus $1.50 per mile. Write the standard form equation that represents the total fare (F) in terms of miles driven (m).

• F = 3m + 1.50

• F = 3 + 1.50m

• F = 3 + 2m

• F = 1.50m

A local bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 12 items and spends $30, write a standard form equation to represent the number of cupcakes (c) and cookies (k) purchased.

• 4c + k = 30, c + k = 10

• 3c + 2k = 30, c + k = 12

• 2c + 3k = 30, c + k = 12

• 3c + k = 30, c + k = 15

A farmer has a total of 100 animals consisting of cows and chickens. If there are twice as many chickens as cows, write a standard form equation to represent the number of cows (c) and chickens (h).

• c + h = 50, h = c

• c + h = 200, h = 3c

• c + h = 100, h = c/2

• c + h = 100, h = 2c

A concert hall has a seating arrangement where the number of rows (r) is 5 less than twice the number of seats per row (s). Write a standard form equation to represent the relationship between rows and seats.

• r + 5 = 2s

• 2s - r = 5

• s = r - 5

• r = 2s + 5

A company produces two types of products: A and B. The total production is limited to 200 units, and product A requires 3 hours to produce while product B requires 2 hours. If the total production time available is 600 hours, write a standard form equation to represent the number of products A (a) and B (b).

• a + b ≤ 200, 3a + 2b ≤ 600

• a + b ≤ 250, 3a + 2b ≤ 700

• a + b = 200, 3a + 2b = 600

• a + b ≤ 150, 3a + 2b ≤ 500

A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If the total revenue from ticket sales is $500 and 60 tickets were sold, write a standard form equation to represent the number of adult tickets (x) and student tickets (y) sold.

• 10x + 5y = 600, x + y = 50

• 5x + 10y = 500, x + y = 60

• 10x + 5y = 500, x + y = 60

• 10x + 5y = 400, x + y = 70