Formulating Linear Equations and Identifying Variables

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) based on the number of miles driven (m). Identify the variables.

• C = 50 + 0.50m

• C = 0.20m - 50

• C = 50 - 0.20m

• C = 50 + 0.20m

A local gym tracks the number of members over the past year. In January, there were 200 members, and by December, there were 300 members. Formulate a linear equation to model the number of members (M) based on the month (t), where January is t=1 and December is t=12.

• M = (100/11)t + 1900/11

• M = (200/11)t + 100/11

• M = (50/11)t + 1500/11

• M = (75/11)t + 1750/11

A farmer sells apples for $2 per pound and has fixed costs of $100. Write a linear equation to represent the total revenue (R) based on the pounds of apples sold (p). Identify the variables in your equation.

• R = 3p

• R = 2p + 100

• R = 2p

• R = p + 100

A school is collecting data on student study hours and their corresponding test scores. If a student studies for 2 hours, they score 75, and if they study for 5 hours, they score 90. Formulate a linear equation to model the relationship between study hours (h) and test scores (s).

• s = 3h + 70

• s = 4h + 80

• s = 10h + 50

• s = 5h + 65

A smartphone company finds that for every $50 increase in price, they sell 100 fewer units. If the current price is $300 and they sell 1,000 units, write a linear equation to represent the number of units sold (u) based on the price increase (p).

• u = 1000 - p

• u = 1000 - 50p

• u = 1000 - 2p

• u = 1000 + 2p

A city’s population is projected to grow from 1 million to 1.5 million over 10 years. Write a linear equation to model the population (P) based on the number of years (y) since the start of the projection.

• P = 0.15y + 1.5

• P = 0.1y + 1

• P = 0.05y + 0.5

• P = 0.05y + 1

A bookstore sells novels for $15 each and has a monthly overhead of $500. Write a linear equation to represent the total profit (P) based on the number of novels sold (n). Identify the variables in your equation.

• P = 20n - 300

• P = 15n + 500

• P = 15n - 500

• P = 10n - 500

A delivery service charges a base fee of $10 plus $1.50 per mile. Write a linear equation to represent the total charge (C) based on the distance traveled (d). Identify the variables in your equation.

• C = 10 + 1.5d

• C = 10 - 1.5d

• C = 10 + 2d

• C = 5 + 1.5d

A tech company’s revenue increased from $200,000 to $300,000 over 5 years. Formulate a linear equation to model the revenue (R) based on the number of years (t) since the start of the period.

• R = 20000t + 200000

• R = 30000t + 200000

• R = 50000t + 200000

• R = 10000t + 200000

A local bakery sells cupcakes for $3 each and has fixed costs of $200. Write a linear equation to represent the total revenue (R) based on the number of cupcakes sold (c). Identify the variables in your equation.

• R = 200 + 3c

• R = 3c + 200

• R = c/3

• R = 3c