Equations Based on Scenarios

An electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. The total cost, C, of the electrician's services can be determined using the function C=65t+70, where t is the number of hours the electrician spends at the house working.

What is theY-INTERCEPT of the function and what is its interpretation in the context of the problem?

• 70; which represents the total cost for all services.

• 70; which represents the set fee for the house call.

• 65; which represents the total cost for all services.

• 65; which represents the set fee for the house call.

When Landon left his house in the morning, his cell phone battery was partially charged. The charge remaining in Landon's battery,B, as a percentage, can be modeled by the function B=-5t+30, where t is the number of hours since Landon left his house.

What is the y-intercept of the function and what is its interpretation in the context of the problem?

• 30; the number of house until Landon's phone dies.

• -5; the charge of the battery when Landon woke up.

• 30; the charge of the battery when Landon left his house.

• -5; the percentage of battery Landon's phone loses each hour.

Samantha is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The function C=125p+400

can be used to determine the total cost,C, in dollars, of producing,p, phones in a given day.

What is the meaning of the slope in the context of the problem?

• the total cost to produce all phones

• the number of phones produced per day

• the additional cost to produce each phone

• the number of days to produce all of the phones

Brandon filled up his car with gas before embarking on a road trip across the country. The number of gallons of gas remaining in his gas tank after t hours of driving can be determined using the equation

G=−1.5t+15.

What is the meaning of the slope of the equation in the context of the problem?

• the number of gallons of gas used per mile

• the initial amount of gas in the tank

• the number of gallons of gas used per hour driven

• the number of hours driven until the gas tank is empty

Bonnie pays a monthly fee of $80 at the health club and an additional $9 every time she attends a yoga class. Which expression below shows her total cost T if she attends y yoga classes this month?

• T = 80 + 9y

• T = 80y + 9

• T = 80 + 9 + y

• T = (80+9)y

Yvette has a home-based business putting on children's parties. She charges $55 to design the party and then $4 per child. Write a function rule that relates the total cost of the party to the number of children n.

• f(n) = 4 + 55n

• f(n) = 4 - 55n

• f(n) = 4n - 55

• f(n) = 55 + 4n

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

• y = 8x + 50

• C = 50m +8

• y = 50x + 8

• C = 8m + 50

A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. Interpret the y-intercept in context.

• The additional fee of $8.

• The initial fee of $25.

• The additional fee of $25.

• The initial fee of $8.

Which of the following situations could be descried by the equation y= -25x + 120

• There are 120 people in the football stadium, and 25 more are entering each hour.

• A plumber charges $25 for a house call and $120 per hour.

• A teacher has 120 students. Her third period has 25 students

• There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

Bob has $150 in his savings account and saves $40 per month.

• y=150 + 40

• y=40x + 150

• y=150x + 40