Solving Real-World Problems with Linear Equations

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

• C = 0.20 + 30m

• C = 30m + 0.20

• C = 30 + 0.20m

• C = 30 - 0.20m

A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If the school sells a total of 200 tickets for $1,500, write a standard form equation to represent the number of adult tickets (a) and student tickets (s).

• a + s = 200, 10a + 5s = 1500

• a + s = 250, 10a + 5s = 1000

• a + s = 100, 10a + 5s = 1200

• a + s = 150, 10a + 5s = 2000

A gardener is planting flowers in a rectangular garden. The length of the garden is 3 feet longer than twice the width. If the total area of the garden is 60 square feet, write a standard form equation to represent the relationship between length (l) and width (w).

• 2w^2 + 3w - 60 = 0

• 2w^2 + 5w - 60 = 0

• w^2 + 3w - 60 = 0

• 2w^2 - 3w - 60 = 0

A bookstore sells novels for $12 each and magazines for $5 each. If a customer buys a total of 15 items and spends $120, write a standard form equation to represent the number of novels (n) and magazines (m) purchased.

• n + m = 20, 10n + 5m = 150

• n + m = 15, 12n + 5m = 120

• n + m = 10, 12n + 5m = 100

• n + m = 15, 10n + 5m = 120

A factory produces two types of toys: action figures and dolls. The factory produces 3 action figures for every 2 dolls. If the total production is 500 toys, write a standard form equation to represent the number of action figures (a) and dolls (d).

• 3d = 2a, a + d = 500

• 4d = 3a

• a + 2d = 500

• 2d = 3a

A local gym charges a monthly fee of $25 plus $10 for each class attended. If a member pays a total of $85 in one month, write a standard form equation to represent the number of classes (c) attended.

• 10c + 15 = 85

• 10c + 25 = 85

• 5c + 25 = 85

• 10c + 30 = 85

A farmer has a total of 100 animals, consisting of cows and chickens. If there are 3 times as many chickens as cows, write a standard form equation to represent the number of cows (c) and chickens (h).

• c + h = 50, h = 2c

• c + h = 100, h = c

• c + h = 200, h = 4c

• c + h = 100, h = 3c

A concert venue has a seating capacity of 1,000. If tickets are sold for $50 each and VIP tickets for $100 each, and the total revenue from ticket sales is $70,000, write a standard form equation to represent the number of regular tickets (r) and VIP tickets (v) sold.

• 50r + 100v = 60000, r + v = 800

• 30r + 70v = 70000, r + v = 1000

• 50r + 100v = 70000, r + v = 1000

• 50r + 100v = 70000, r + v = 1200

A pizza shop sells two sizes of pizzas: small and large. A small pizza costs $8 and a large pizza costs $12. If a customer buys a total of 10 pizzas for $88, write a standard form equation to represent the number of small pizzas (s) and large pizzas (l) purchased.

• 8s + 12l = 88, s + l = 10

• 7s + 10l = 88, s + l = 9

• 6s + 12l = 88, s + l = 12

• 8s + 10l = 88, s + l = 11

A charity event is selling two types of raffle tickets: regular tickets for $2 and premium tickets for $5. If they sold a total of 300 tickets and raised $1,200, write a standard form equation to represent the number of regular tickets (r) and premium tickets (p) sold.

• 2r + 5p = 1000, r + p = 350

• 2r + 5p = 1200, r + p = 300

• 3r + 4p = 1200, r + p = 250

• r + 2p = 1200, r + p = 300