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

Answer 1

This question is based on the concept of solving a two linear equation.

Thus, the cost of one bath towel is $9 and one hand towel is $4.

Given:

Number of  ordered of hand towels is 27 and bath towels is 48 and for a bill of $540 for the first hotel.

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

We need tom determined the cost of one hand towel and one bath towel.

According to the question:

Let the  hand towels be h  and bath towels be b.

Therefore, equation of first hotel is

27h + 48b = 540........(1)

Equation of second hotel is

50h + 24b = 416.........(2)

Now, solving both equation for h and b.

Equation (2) multiplying by -2.

-100 h -48 b = - 832..................(3)

Now, solve equation (1) and (3)

27h + 48b = 540  and -100h - 48b = - 832

⇒ -73 h = - 292

⇒ h = -292 / -73

⇒ h = 4

Therefore, the cost of 1 hand towel is $4.

Now, putting the value of h = 4 in equation (1).

⇒ 27(4) + 48b = 540

⇒ 108 + 48b = 540

⇒ 48b = 540 - 108

⇒ 48b = 432

⇒ b = 432/48

⇒ b = 9

Therefore, the cost of 1 bath towel is $9.

Thus, the cost of one bath towel is $9 and one hand towel is $4.

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