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Vanessa has a $900 travel and lodging budget for her vacation. She found round-trip plane tickets for x dollars total, a hotel for y dollars per night, and free shuttle service between the airport and the hotel. If she plans to stay at the hotel for 5 nights, and she spends less than what she budgeted on travel and lodging, which of the following inequalities best describes the scenario? Choose 1 answer: (A) x+5y > 900 (B) 5x+y > 900 (C) x+5y < 900 (D) 5x+y < 900

Vanessa has a $900 \$ 900 travel and lodging budget for her vacation. She found round-trip plane tickets for x x dollars total, a hotel for y y dollars per night, and free shuttle service between the airport and the hotel. If she plans to stay at the hotel for 55 nights, and she spends less than what she budgeted on travel and lodging, which of the following inequalities best describes the scenario?\newlineChoose 11 answer:\newline(A) x+5 y>900 \newline(B) 5 x+y>900 \newline(C) x+5 y<900 \newline(D) 5 x+y<900

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Q. Vanessa has a $900 \$ 900 travel and lodging budget for her vacation. She found round-trip plane tickets for x x dollars total, a hotel for y y dollars per night, and free shuttle service between the airport and the hotel. If she plans to stay at the hotel for 55 nights, and she spends less than what she budgeted on travel and lodging, which of the following inequalities best describes the scenario?\newlineChoose 11 answer:\newline(A) x+5y>900 x+5 y>900 \newline(B) 5x+y>900 5 x+y>900 \newline(C) x+5y<900 x+5 y<900 \newline(D) 5x+y<900 5 x+y<900
  1. Identify variables and meanings: Identify the variables and their meanings. Vanessa's total budget for travel and lodging is $900\$900. The cost of the round-trip plane tickets is represented by xx dollars, and the cost of the hotel per night is represented by yy dollars. Vanessa plans to stay at the hotel for 55 nights. We need to express the total cost of the plane tickets and the hotel stay in terms of xx and yy.
  2. Calculate hotel stay cost: Calculate the total cost of the hotel stay. Since Vanessa is staying for 55 nights and the hotel costs yy dollars per night, the total cost for the hotel stay is 55 times yy, which is 5y5y dollars.
  3. Combine costs for total travel and lodging: Combine the costs of the plane tickets and the hotel stay to find the total travel and lodging cost. The total cost is the sum of the plane tickets cost xx and the hotel stay cost 5y5y, which gives us x+5yx + 5y dollars.
  4. Formulate budget inequality: Formulate the inequality based on Vanessa's budget. Vanessa wants to spend less than her budget of $900\$900 on travel and lodging. Therefore, the total cost of travel and lodging, which is x+5yx + 5y, must be less than $900\$900. The inequality that represents this situation is x + 5y < 900.
  5. Match correct inequality: Match the correct inequality with the given choices. The inequality we have found is x + 5y < 900, which corresponds to choice (C).

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