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?

Answer 1

H=$hand towel, B=$bath towel.
27H+48B=540, 50H+24B=416, so 100H+48B=832;
100H+540-27H=832; 73H=832-540=292, H=292/73=$4.
48B=540-27×4=540-108=432, B=432/48=$9.
Hand towels are $4 each, and bath towels are $9 each.

Answer 2

Answer:

The cost of the hand towel is $4 and the cost of the bath towel is $9 .

Step-by-step explanation

Let us assume that the cost of one hand towel be x .

Let us assume that the cost of one bath towel be y .

As given

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.

Equation become

Cost of one hand towels × Order of number of hand towels + Cost of one bath towels × Order of number of bath towels = Total cost

Put all the values in the above

27x + 48y = 540

As given

He ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel.

Equation becomes

50x + 24y = 416

Multiply 27x + 48y = 540  by 50

we get

1350x + 2400y = 27000

Multiply 50x + 24y = 416 by 27

1350x + 648y = 11232

Subtracted 1350x + 648y = 11232  from 1350x + 2400y = 27000 .

1350x - 1350x + 2400y - 648y = 27000 - 11232

1752y = 15768

$y = \frac{15768}{1752}$

y = 9

Put this value in the equation 50x + 24y = 416 .

50x + 24 × 9 = 416

50x + 216 = 416

50x = 200

$x = \frac{200}{50}$

x = 4

Therefore the cost of the hand towel is $4 and the cost of the bath towel is $9 .