A tour director is hiring boats to transport a group of tourists across a river. He must make sure there is room for at least 27 passengers, the number of tourists in the group. A dinghy can seat 5 passengers and a flatboat can seat 2 passengers. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. x = the number of dinghies y = the number of flatboats Choices: (A)5x + 2y 27 (B)5x + 2y

Question

A tour director is hiring boats to transport a group of tourists across a river. He must make sure there is room for at least 27 passengers, the number of tourists in the group. A dinghy can seat 5 passengers and a flatboat can seat 2 passengers.  Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. x = the number of dinghies y = the number of flatboats     Choices: (A)5x + 2y > 27 (B)5x + 2y < 27 (C)5x + 2y ≤ 27 (D)5x + 2y ≥ 27

Bytelearn · Accepted Answer

Define variables: Define the variables based on the given information. The number of dinghies is represented by x, and each dinghy can seat 5 passengers. Therefore, the total number of passengers that can be seated in dinghies is 5x. Define seating capacities: Similarly, define the variable for the number of flatboats, which is represented by y, and each flatboat can seat 2 passengers. Therefore, the total number of passengers that can be seated in flatboats is 2y. Combine total capacities: Combine the total seating capacities of dinghies and flatboats to represent the total number of passengers that can be transported. This is done by adding the expressions from Step 1 and Step 2, resulting in 5x + 2y. Set minimum passenger requirement: Since the tour director needs to transport at least 27 passengers, the combined seating capacity of dinghies and flatboats must be greater than or equal to 27. This leads to the inequality 5x + 2y ≥ 27.

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