Question

des 1: The number of tables in the restaurant is equal to one-third the number of chairs
write the des 1 inverse
des 2: The number of tables in the restaurant is equal to three times the number of servers
write des 2 inverese
The number of chairs in the restaurant is equal to three times the number of tables.
Write the des 3 Inverse:
Which two descriptions are inverse of each other?

Answer 1

To write the inverse of a description, we typically express it in terms of the opposite relationship.

### Original Descriptions
1. **Des 1:** The number of tables in the restaurant is equal to one-third the number of chairs.
2. **Des 2:** The number of tables in the restaurant is equal to three times the number of servers.
3. **Des 3:** The number of chairs in the restaurant is equal to three times the number of tables.

### Inverses
1. **Des 1 Inverse:** The number of chairs in the restaurant is equal to three times the number of tables.
(This is essentially Des 3.)

2. **Des 2 Inverse:** The number of servers in the restaurant is equal to one-third the number of tables.

3. **Des 3 Inverse:** The number of tables in the restaurant is equal to one-third the number of chairs.
(This is essentially Des 1.)

### Which Two Descriptions are Inverse of Each Other?
Des 1 and Des 3 are inverses of each other:

- **Des 1:** \( T = \frac{1}{3}C \) → This means \( C = 3T \) (Des 3).
- **Des 3:** \( C = 3T \) → This means \( T = \frac{1}{3}C \) (Des 1).

Thus, Des 1 and Des 3 are indeed inverses of one another.