Final answer:
To find the towel costs, a system of equations is set up using the given expenses for hand and bath towels. Upon solving the system, it is determined that the cost of a hand towel is approximately $4 and a bath towel approximately $6.
Step-by-step explanation:
The question involves setting up a system of equations to find the towel cost for both hand towels and bath towels for an owner who is ordering towels for two hotels.
Let's use the variables h to represent the cost of a hand towel and b for the cost of a bath towel. We can set up two equations based on the information provided:
5h + 61b = $368 (Hillsboro order)
91h + 61b = $730 (Salem order)
To solve this system, we can multiply the first equation by -1 to help us eliminate one variable when we add the two equations:
-5h - 61b = -$368
91h + 61b = $730
Adding the two equations gives us 86h = $362, so h (cost of a hand towel) = $362 / 86 = $4.21 (approximately, but since we need a whole number based on the options, this indicates $4). Using this value of h in the first equation, we get 5(4) + 61b = $368, which simplifies to $20 + 61b = $368, and then 61b = $348, which gives us b = $348 / 61 = $5.70 (approximately, but since we need a whole number based on the options, this indicates $6). Therefore, the cost of each hand towel is $4 and each bath towel is $6.