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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...Question
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
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
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Answered by
GPT-4o mini
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:
\[
x + 5y < 2700
\]
- \( x \) = 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:
\[
x + 5y < 2700
\]
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