A hotel buyer is ordering new towels for all of the rooms in the hotel. Hand towels cost $1 apiece and bath towels cost $5. 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

1 answer

To represent the situation with an inequality in standard form, we can use the given variables:

  • \( x \) = the number of hand towels ordered
  • \( y \) = the number of bath towels ordered

The costs for the towels are as follows:

  • Each hand towel costs $1, so the total cost for hand towels is \( 1x \) (or simply \( x \)).
  • Each bath towel costs $5, so the total cost for bath towels is \( 5y \).

The total expenditure for the towels must be under $2,700, which can be expressed as:

\[ x + 5y < 2700 \]

To express this in standard form (Ax + By < C), we have:

\[ x + 5y < 2700 \]

In this case, \( A = 1 \), \( B = 5 \), and \( C = 2700 \).

If you are specifically looking for a standard form representation where the inequality is written with all terms on one side, you could rearrange it as:

\[ x + 5y - 2700 < 0 \]

That's the inequality describing the situation in standard form.

So, the final inequality is:

\[ x + 5y < 2700 \]