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Consider the following descriptions, each representing a relation.

Description #1: The number of chairs in the restaurant is equal to three times the number of tables.

Description #2: The number of tables in the restaurant is equal to one-third the number of chairs.

Description #3: The number of tables in the restaurant is equal to three times the number of servers.

Question 1
A. Identify the two descriptions that represent relations that are inverses. (2 points)
Description # and Description #
Question 2
B. Create a verbal description for the inverse of description whose inverse is not given,(2 points)

1 answer

To determine which descriptions represent inverse relations, let's first analyze the given relations:

  1. Description #1: The number of chairs (C) in the restaurant is equal to three times the number of tables (T).

    • This can be represented as: \( C = 3T \)

  2. Description #2: The number of tables (T) in the restaurant is equal to one-third the number of chairs (C).

    • This can be represented as: \( T = \frac{1}{3}C \)
    • This is the inverse of Description #1 because it expresses the relationship in terms of T instead of C.

  3. Description #3: The number of tables (T) in the restaurant is equal to three times the number of servers (S).

    • This can be represented as: \( T = 3S \)

Now, let's answer the questions:

Question 1

A. Identify the two descriptions that represent relations that are inverses.

  • Description #1 and Description #2.

Question 2

B. Create a verbal description for the inverse of the description whose inverse is not given.

  • Description #3 does not have an inverse given. Its inverse can be described as follows:

"The number of servers in the restaurant is equal to one-third the number of tables."

This can be expressed mathematically as \( S = \frac{1}{3}T \), which is the inverse of Description #3.