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 45 passengers, the number of tourists in the group. a dinghy can seat 6 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

Answer 1

The inequality describing the situation where at least 45 passengers must be transported using dinghies and flatboats is 6x + 2y ≥ 45, where x is the number of dinghies, and y is the number of flatboats.

Step-by-step explanation:

The inequality in standard form that describes the situation where a tour director needs to transport at least 45 passengers using dinghies and flatboats is:

6x + 2y ≥ 45

Here, x represents the number of dinghies, each seating 6 passengers, and y represents the number of flatboats, each seating 2 passengers. The inequality ensures that the total number of passengers that can be seated is at least 45.

Step-by-step explanation:

1. Let the variable x represent the number of dinghies.
2. Let the variable y represent the number of flatboats.
3. Since each dinghy can seat 6 passengers, we use 6x to represent the passengers seated in dinghies.
4. Since each flatboat can seat 2 passengers, we use 2y to represent the passengers seated in flatboats.
5. Add the two expressions to account for all the passengers: 6x + 2y.
6. Since there must be room for at least 45 passengers, we use the inequality ≥ to indicate 'at least' or 'no less than'.
7. Combine all elements to form the inequality: 6x + 2y ≥ 45.

Answer 2

The inequality in standard form for the tour director's problem, with 'x' representing dinghies and 'y' representing flatboats, is 6x + 2y >= 45.

Step-by-step explanation:

The tour director needs to ensure that there is seating available for at least 45 passengers using dinghies and flatboats. A dinghy can seat 6 passengers, and a flatboat can seat 2 passengers. We can use the variables x for the number of dinghies and y for the number of flatboats. The inequality that describes this situation in standard form is 6x + 2y ≥ 45. This inequality ensures that the total number of passengers that can be transported across the river, given the seating capacity of each type of boat, is at least 45.