Translating Real-Life Scenarios into Linear Equations

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an equation to represent the total cost (C) of renting a car for x miles driven.

• C = 50 - 0.20x

• C = 50 + 0.50x

• C = 0.20 + x

• C = 50 + 0.20x

Maria is saving money to buy a new phone. She currently has $150 and saves $25 each week. Write an equation to represent the total amount of money (M) she will have after w weeks.

• M = 25w - 150

• M = 150 + 25w

• M = 150 - 25w

• M = 150 + 50w

A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If the school sells a total of 100 tickets for $800, write an equation to represent the relationship between adult tickets (a) and student tickets (s).

• 10a + 5s = 1000, a + s = 80

• 10a + 5s = 800, a - s = 20

• 10a + 5s = 800, a + s = 100

• 5a + 10s = 800, a + s = 100

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 an equation to represent the number of apples (a) and oranges (o) he bought.

• a + o = 8, 2a + 3o = 30

• a + o = 10, 2a + 3o = 24

• a + o = 10, 2a + 3o = 18

• a + o = 12, 2a + 3o = 20

A gym charges a monthly fee of $30 plus $5 for each class attended. Write an equation to represent the total cost (T) for attending c classes in a month.

• T = 30c + 5

• T = 5 + 30c

• T = 30 - 5c

• T = 30 + 5c

A bookstore sells notebooks for $3 each and pens for $2 each. If a student buys a total of 15 items for $36, write an equation to represent the number of notebooks (n) and pens (p) purchased.

• n + p = 10, 3n + 2p = 30

• n + p = 20, 3n + 2p = 40

• n + p = 15, 2n + 3p = 36

• n + p = 15, 3n + 2p = 36

A gardener is planting flowers in rows. Each row can hold 8 flowers. If the gardener has a total of 64 flowers, write an equation to find the number of rows (r) needed.

• 12

• 10

• 8

• 6

A factory produces 500 toys in 5 hours. If the production rate is constant, write an equation to represent the number of toys (T) produced in h hours.

• T = 200h

• T = 50h

• T = 500h

• T = 100h

A concert hall has 200 seats. If adult tickets cost $15 and student tickets cost $10, and the total revenue from ticket sales is $2,500, write an equation to represent the number of adult tickets (a) and student tickets (s) sold.

• a + s = 150, 15a + 10s = 2000

• a + s = 200, 20a + 5s = 2500

• a + s = 250, 15a + 10s = 3000

• a + s = 200, 15a + 10s = 2500

A train travels at a speed of 60 miles per hour. Write an equation to represent the distance (D) traveled in t hours.

• D = 60t^2

• D = 60 + t

• D = 60t

• D = 30t