Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The owner of two hotels is ordering towels. He bought 15 hand towels and 93 bath towels for his hotel in Princeton, spending a total of $1,098. He also ordered 74 hand towels and 72 bath towels for his hotel in Lancaster, spending $1,162. How much does each towel cost? A hand towel costs $_____, and a bath towel costs $_____.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  The owner of two hotels is ordering towels. He bought 15 hand towels and 93 bath towels for his hotel in Princeton, spending a total of $1,098. He also ordered 74 hand towels and 72 bath towels for his hotel in Lancaster, spending $1,162. How much does each towel cost?  A hand towel costs $_____, and a bath towel costs $_____.

Bytelearn · Accepted Answer

Define variables: Let's define two variables: let x be the cost of one hand towel and y be the cost of one bath towel. We can then write two equations based on the information given: 1) For the Princeton hotel: 15x + 93y = 1,098 2) For the Lancaster hotel: 74x + 72y = 1,162Use elimination method: To use elimination, we need to eliminate one of the variables. We can do this by multiplying the first equation by a number that will make the coefficient of x or y in both equations the same. Let's multiply the first equation by 74 and the second equation by 15, so the coefficients of x will be the same. First equation multiplied by 74: (15x + 93y) * 74 = 1,098 * 74 Second equation multiplied by 15: (74x + 72y) * 15 = 1,162 * 15Perform multiplication: Now let's perform the multiplication: First equation: 1110x + 6882y = 81,252 Second equation: 1110x + 1080y = 17,430Eliminate variable x: Next, we subtract the second equation from the first to eliminate x: (1110x + 6882y) - (1110x + 1080y) = 81,252 - 17,430 This simplifies to: 6882y - 1080y = 81,252 - 17,430Solve for y: Now we solve for y: 5802y = 63,822 y = 63,822 / 5802 y = 11 So, each bath towel costs $11.Substitute y into equation: Now that we know the cost of each bath towel, we can substitute y = 11 into one of the original equations to find x. Let's use the first equation: 15x + 93y = 1,098 15x + 93(11) = 1,098Solve for x: Now we solve for x: 15x + 1023 = 1,098 15x = 1,098 - 1023 15x = 75 x = 75 / 15 x = 5 So, each hand towel costs $5.

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