Chapter 8.9, Problem 32E

a.

To determine

To write:

An inequality describing the possible numbers of 1-ticket rides and 2-ticket rides that you can go on.

Answer to Problem 32E

The inequality $x+2y\le 20$ represents the possible numbers of 1-ticket rides and 2-ticket rides that you can go on.

Explanation of Solution

Given:

At a country fair, you buy 20 tickets that you can use for carnival rides and other attractions. Some rides require 1 ticket while others require 2 tickets.

Calculation:

Let x represent number of 1-ticket rides and y represent number of 2-ticket rides.

We have been given that some rides require 1 ticket, so number of tickets used in x rides would be x .

We are also told that some rides require 2 tickets,so number of tickets used in yrides would be $2y$ .

Since you have total 20 tickets, so sum of total tickets used in all rides would be less than or equal to 20. We can represent this information in an inequality as:

  $x+2y\le 20$

Therefore, the inequality $x+2y\le 20$ represents the possible numbers of 1-ticket rides and 2-ticket rides that you can go on.

b.

To determine

To graph:

The inequality from part (a).

Answer to Problem 32E

Our required graph would look like:

  

Explanation of Solution

Given:

At a country fair, you buy 20 tickets that you can use for carnival rides and other attractions. Some rides require 1 ticket while others require 2 tickets.

Calculation:

Upon graphing our given inequality, we will get our required graph as shown below:

  

c.

To determine

To give:

Three possible combinations for 1-ticket rides and 2-ticket rides that you can go on.

Answer to Problem 32E

You can go on 2 one-ticket rides and 9 two-ticket rides, or 8 one-ticket rides and 6 two-ticket rides, or 10 one-ticket rides and 5 two-ticket rides.

Explanation of Solution

Given:

At a country fair, you buy 20 tickets that you can use for carnival rides and other attractions. Some rides require 1 ticket while others require 2 tickets.

Calculation:

Upon looking at graph of our inequality in part (b), we can see that points $(2,9),(8,6)\text{ and (10,5)}$ satisfy our inequality. Therefore, you can go on2 one-ticket rides and 9 two-ticket rides, or 8 one-ticket rides and 6 two-ticket rides, or 10 one-ticket rides and 5 two-ticket rides.