Algebra 2: Word Problems in Functions & Systems of Equations

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write a function to represent the total cost of renting a car based on the miles driven. How much would it cost to drive 150 miles?

• $75

• $50

• 60

• $100

The graph of a function shows that the revenue (in dollars) from selling x items is represented by R(x) = 50x - 200. How many items must be sold to break even?

• 4

• 10

• 6

• 2

Two friends, Alice and Bob, are saving money to buy a video game. Alice saves $5 a week, while Bob saves $3 a week. If they start with $20 and $10 respectively, write a system of equations to represent their savings over time. How many weeks will it take for Alice to have more money than Bob?

• 3

• 0

• 2

• 1

A store sells two types of shirts: plain and printed. The plain shirts cost $15 each, and the printed shirts cost $25 each. If a customer buys a total of 10 shirts for $200, set up a system of equations to find out how many of each type of shirt was purchased.

• 6 plain shirts and 4 printed shirts

• 5 plain shirts and 5 printed shirts

• 8 plain shirts and 2 printed shirts

• 7 plain shirts and 3 printed shirts

The height of a ball thrown into the air can be modeled by the function h(t) = -16t^2 + 32t + 5, where h is the height in feet and t is the time in seconds. What is the maximum height reached by the ball?

• 21 feet

• 15 feet

• 18 feet

• 25 feet

A farmer has a rectangular field that is 3 meters longer than it is wide. If the perimeter of the field is 36 meters, write a system of equations to find the dimensions of the field.

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

• Width: 7.5 meters, Length: 10.5 meters

• Width: 6 meters, Length: 9 meters

The graph of a linear function shows that the cost of a subscription service is $10 per month plus a one-time fee of $50. Write a function to represent the total cost after x months. How much will the total cost be after 6 months?

• $120

• $60

• $110

• $100

A school is planning a field trip and has a budget of $500. The cost per student is $25, and there is a fixed cost of $100 for the bus. Write an equation to determine how many students can attend the trip within the budget.

• 10

• 16

• 20

• 25

A local bakery sells cupcakes for $2 each and cookies for $1 each. If a customer buys a total of 20 items and spends $30, set up a system of equations to find out how many cupcakes and cookies were purchased.

• 5 cupcakes and 15 cookies

• 12 cupcakes and 8 cookies

• 10 cupcakes and 10 cookies

• 15 cupcakes and 5 cookies

The temperature in a city can be modeled by the function T(t) = -2t^2 + 12t + 5, where T is the temperature in degrees Celsius and t is the time in hours. What is the temperature at t = 3 hours?

• 20 degrees Celsius

• 15 degrees Celsius

• 30 degrees Celsius

• 23 degrees Celsius