Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. The owner of two hotels is ordering towels. He bought 14 hand towels and 41 bath towels for his hotel in Kensington, spending a total of $521. He also ordered 50 hand towels and 45 bath towels for his hotel in Yardley, spending $745. 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 any method, and fill in the blanks.  The owner of two hotels is ordering towels. He bought 14 hand towels and 41 bath towels for his hotel in Kensington, spending a total of $521. He also ordered 50 hand towels and 45 bath towels for his hotel in Yardley, spending $745. How much does each towel cost?  A hand towel costs $_____, and a bath towel costs $_____.

Bytelearn · Accepted Answer

Define Costs: Let's denote the cost of a hand towel as x dollars and the cost of a bath towel as y dollars. The first equation represents the total cost of hand towels and bath towels for the Kensington hotel: 14x + 41y = 521Equations for Hotels: The second equation represents the total cost of hand towels and bath towels for the Yardley hotel: 50x + 45y = 745Elimination Method: We now have a system of two equations with two variables: 14x + 41y = 521 50x + 45y = 745 We can solve this system using either substitution or elimination. Let's use the elimination method to eliminate one of the variables.Multiply and Align Coefficients: Multiply the first equation by 50 and the second equation by 14 to align the coefficients of x: (14x + 41y) * 50 = 521 * 50 (50x + 45y) * 14 = 745 * 14 This gives us: 700x + 2050y = 26050 700x + 630y = 10430Subtract to Eliminate x: Subtract the second new equation from the first new equation to eliminate x: (700x + 2050y) - (700x + 630y) = 26050 - 10430 700x + 2050y - 700x - 630y = 26050 - 10430 1420y = 15620Solve for y: Solve for y by dividing both sides of the equation by 1420: y = 15620 / 1420 y = 11Substitute Back for x: Now that we have the value of y, we can substitute it back into one of the original equations to find x. Let's use the first original equation: 14x + 41(11) = 521 14x + 451 = 521Solve for x: Subtract 451 from both sides of the equation to solve for x: 14x = 521 - 451 14x = 70Final Cost Calculation: Divide both sides of the equation by 14 to find the value of x: x = 70 / 14 x = 5We have found the cost of each hand towel and each bath towel: A hand towel costs $5, and a bath towel costs $11.

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