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?

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 = 9

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

50x + 24 × 9 = 416

50x + 216 = 416

50x = 200

x = 4

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

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step-by-step explanation: