Question

A hotel buyer is ordering new towels for all of the rooms in the hotel. Hand towels cost $2 apiece and bath towels cost $4. The total expenditure must be under $2,700.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of hand towels ordered
y = the number of bath towels ordered

Answer 1

To express the situation as an inequality, let's use the variables you've defined:

- \( x \): the number of hand towels ordered
- \( y \): the number of bath towels ordered

The cost of the hand towels is $2 each, so the total cost for hand towels can be expressed as \( 2x \).
The cost of the bath towels is $4 each, so the total cost for bath towels can be expressed as \( 4y \).

We need to ensure that the total expenditure for towels is under $2,700. Therefore, the inequality representing this situation is:

\[
2x + 4y < 2700
\]

To express this inequality in standard form (which is typically written as \( Ax + By \leq C \), or \( Ax + By < C \)), we can rearrange it to match that format:

\[
2x + 4y < 2700
\]

This inequalities is already in standard form, so you can use it as is:

\[
\boxed{2x + 4y < 2700}
\]