Question

You are planning a school field trip to a local theater. It costs $\$ 60$ to rent the bus. Each theater ticket costs $55.50 .$ a. Write a function $c(x)$ to represent the cost per student if $x$ students sign up. b. How many students must sign up if the cost is to be no more than $\quad \$ 10$ per student?

Name: Problem 34, Chapter 9: Algebra 2
Uploaded: 2020-03-20T20:12:14-08:00
Duration: 1 min 43 s
Channel: Joshua Eastwood
Description: You are planning a school field trip to a local theater. It costs 60 to rent the bus. Each theater ticket costs 55.50 . a. Write a function c(x) to represent the cost per student if x students sign up. b. How many students must sign up if the cost is to be no more than 10 per student?

   You are planning a school field trip to a local theater. It costs $\$ 60$ to rent the bus. Each theater ticket costs $55.50 .$
a. Write a function $c(x)$ to represent the cost per student if $x$ students sign up.
b. How many students must sign up if the cost is to be no more than $\quad \$ 10$ per student?

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 9, Problem 34

Instant Answer

Solved by Expert Joshua Eastwood

03/20/2020

Step 1

The total cost of the trip is the sum of the cost of the bus and the cost of the theater tickets for all students. The cost of the bus is a fixed cost of $60, and the cost of the theater tickets is $55.50 per student. So, the total cost is $60 + 55.50x$. To find Show more…

Show all steps

Thanks for your feedback!

You are planning a school field trip to a local theater. It costs $\$ 60$ to rent the bus. Each theater ticket costs $55.50 .$ a. Write a function $c(x)$ to represent the cost per student if $x$ students sign up. b. How many students must sign up if the cost is to be no more than $\quad \$ 10$ per student?

Play audio

Feedback

Joshua Eastwood and 80 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Function Modeling

Constructing mathematical functions to represent real-world relationships is crucial. In cost problems, a function can be used to combine different cost elements (such as fixed and variable costs) into one expression that models how the cost per participant changes with the number of participants.

Fixed and Variable Costs

Understanding fixed costs (which remain constant regardless of the number of participants) and variable costs (which increase proportionally with each participant) is key. This concept allows one to break down and accurately represent the overall cost structure of a process or event.

Inequality Solving

Setting up and solving inequalities is important when there is a need to determine how many units (or participants) are required to meet a specific cost constraint. This involves using algebraic manipulation to isolate the variable and find the range of values that keeps the cost within prescribed limits.

Please give Ace some feedback