Question

A hotel manager is ordering new towels for all of the rooms in the hotel. Hand towels cost $2 and bath towels cost $5. The total expenditure must be under $5,200. Let x be the number of hand towels ordered and y be the number of bath towels ordered. Which inequality in standard form represents this situation?

1) 2x + 5y < 5,200
2) 2x + 5y ≤ 5,200
3) 2x5y < 5,200
4) 2x5y ≤ 5,200

Answer 1

The inequality in standard form that represents the situation of ordering hand towels and bath towels while staying under a budget of $5,200 is 2x + 5y < 5,200.

Step-by-step explanation:

To represent the situation where a hotel manager is ordering new towels with a total expenditure under $5,200, where hand towels cost $2 each and bath towels cost $5 each, you would use a linear inequality in two variables. Let x be the number of hand towels and y be the number of bath towels ordered. The cost for hand towels is then 2x and for bath towels 5y. The total cost is the sum of these two amounts and must be less than $5,200.

Therefore, the inequality representing this situation is:
2x + 5y < 5,200.

This is in standard form, which is Ax + By < C, where A, B, and C are constants. The inequality shows that the combined cost of hand towels and bath towels should be less than $5,200 to satisfy the manager's budget constraint.