Word Problems: Setting Up Equations for Cost & Change

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) based on the number of miles driven (m). What is the initial value and the rate of change?

• C = 30 + 0.20m; Initial value: 30; Rate of change: 0.20

• C = 50 + 0.50m; Initial value: 50; Rate of change: 0.50

• C = 50 + 0.10m; Initial value: 50; Rate of change: 0.10

• C = 50 + 0.20m; Initial value: 50; Rate of change: 0.20

A phone plan costs $30 per month plus $0.10 per text message. If a customer sends 150 text messages in a month, how much will they pay? Set up the equation and identify the initial value and rate of change.

• $60

• $30

• $45

• $15

A bakery sells cupcakes for $3 each and has a fixed cost of $20 for supplies. Write an equation for the total revenue (R) based on the number of cupcakes sold (c). What do the initial value and rate of change represent in this context?

• R = 3c + 10

• R = 20 + 3c

• R = 5c

• R = 3c

A gym membership costs $40 to join and $25 per month. If a member has been with the gym for 6 months, how much have they spent in total? Set up the equation and identify the initial value and rate of change.

• $180

• $150

• $190

• $210

A school is selling tickets for a play at $10 each, with an initial cost of $100 for the venue. Write an equation for the total revenue (R) based on the number of tickets sold (t). What do the initial value and rate of change indicate?

• R = 5t

• R = 10t + 100

• R = 10t

• R = 100 + 10t

A water tank starts with 500 liters of water and loses 5 liters per hour due to a leak. Write an equation to represent the amount of water (W) in the tank after h hours. What is the initial value and the rate of change?

• Initial value: 500 liters, Rate of change: -5 liters/hour

• Initial value: 500 liters, Rate of change: 5 liters/hour

• Initial value: 0 liters, Rate of change: -10 liters/hour

• Initial value: 1000 liters, Rate of change: -5 liters/hour

A delivery service charges a base fee of $15 plus $2 per mile. If a customer wants to send a package 10 miles, how much will it cost? Set up the equation and identify the initial value and rate of change.

• $50

• $45

• $35

• $25

A subscription service charges $10 per month with an initial sign-up fee of $20. If a user subscribes for 3 months, how much will they pay in total? Write the equation and explain the initial value and rate of change.

• $30

• $50

• $40

• $60

A farmer sells apples for $2 each and has a fixed cost of $50 for equipment. Write an equation for the total income (I) based on the number of apples sold (a). What do the initial value and rate of change represent?

• I = 2a - 100

• I = 2a - 50

• I = 2a + 50

• I = 3a - 50

A taxi company charges a flat rate of $3 plus $1.50 per mile. If a passenger travels 5 miles, how much will the fare be? Set up the equation and identify the initial value and rate of change.

• $9.50

• $12.00

• $8.00

• $10.50