Question

A motel is purchasing new towels. Suites require 12 towels and individual rooms require 4 towels. The minimum order required by the towel vendor is 630 towels.
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of suites receiving new towels
y = the number of individual rooms receiving new towels

Answer 1

To formulate the inequality that describes the situation of towel orders for the motel, we need to express the total number of towels required by both suites and individual rooms based on the variables given:

- Each suite requires 12 towels, so for \( x \) suites, the total number of towels required is \( 12x \).
- Each individual room requires 4 towels, so for \( y \) individual rooms, the total number of towels required is \( 4y \).

The total number of towels required by both the suites and individual rooms can be expressed as:

\[
12x + 4y
\]

According to the problem, the motel needs to order a minimum of 630 towels. This requirement can be written as the inequality:

\[
12x + 4y \geq 630
\]

To express this inequality in standard form (Ax + By ≤ C), we can rearrange it:

1. Move \( 630 \) to the left side:

\[
12x + 4y - 630 \geq 0
\]

2. Multiply the entire inequality by \(-1\) to change the direction (this also makes it standard form):

\[
-12x - 4y \leq -630
\]

For standard form \( Ax + By \leq C \), it's common to have A as a positive number. Thus, we can multiply the whole inequality by \(-1\):

\[
12x + 4y \geq 630
\]

This results in the inequality:

\[
12x + 4y \geq 630
\]

In standard form, it represents the minimum order of towels required, ensuring the right number of towels for both suites and individual rooms.