Select the correct answer.

Question

Mr. Miller owns two hotels and is ordering towels for the rooms. He ordered 27 hand towels and 48 bath towels for a bill of $540 for the first hotel. He ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel.

What is the cost of one hand towel and one bath towel?

A.
The cost of one hand towel is $4 and the cost of one bath towel is $9.
B.
The cost of one hand towel is $9 and the cost of one bath towel is $4.
C.
The cost of one hand towel is $8 and the cost of one bath towel is $5.
D.
The cost of one hand towel is $5 and the cost of one bath towel is $8.

Answer 1

Let \( h \) represent the cost of one hand towel and \( b \) represent the cost of one bath towel.

From the information provided, we can set up the following system of equations based on Mr. Miller's orders:

1. For the first hotel: \[ 27h + 48b = 540 \quad \text{(Equation 1)} \]

2. For the second hotel: \[ 50h + 24b = 416 \quad \text{(Equation 2)} \]

We can solve this system of equations to find the values of \( h \) and \( b \).

First, let's multiply Equation 1 by 2 to facilitate elimination: \[ 54h + 96b = 1080 \quad \text{(Equation 3)} \]

Next, multiply Equation 2 by 4: \[ 200h + 96b = 1664 \quad \text{(Equation 4)} \]

Now we can subtract Equation 3 from Equation 4: \[ (200h + 96b) - (54h + 96b) = 1664 - 1080 \] \[ 200h - 54h = 584 \] \[ 146h = 584 \] \[ h = \frac{584}{146} = 4 \]

Now that we have \( h = 4 \), we can substitute this value back into one of the original equations to find \( b \). Using Equation 1: \[ 27(4) + 48b = 540 \] \[ 108 + 48b = 540 \] \[ 48b = 540 - 108 \] \[ 48b = 432 \] \[ b = \frac{432}{48} = 9 \]

Thus, the cost of one hand towel is \( \mathbf{4} \) and the cost of one bath towel is \( \mathbf{9} \).

Therefore, the correct answer is: A. The cost of one hand towel is $4 and the cost of one bath towel is $9.