Formulate a system of inequalities to represent the given situation about passengers and maintenance costs.

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ScanSolve AI Tutor · Accepted Answer

Step 1: Define variables based on the problem statement. Let x be the number of passengers in the mini-bus. Let y be the number of passengers in the car. Step 2: Formulate the inequality for the total maintenance cost. The maintenance cost per passenger for the bus is 2.00, so for x$ passengers, the cost is 2x. The maintenance cost per passenger for the car is 3.00, so for y$ passengers, the cost is 3y. The total maintenance cost must not exceed 45. 2x + 3y ≤ 45 Step 3: Formulate the inequality for the total number of passengers. The total number of passengers (bus + car) must not be more than 20. x + y ≤ 20 Step 4: Formulate non−negativity inequalities. The number of passengers cannot be negative. x ≥ 0 y ≥ 0 The inequalities connecting x and y$ are: 2x + 3y ≤ 45 x + y ≤ 20 x ≥ 0 y ≥ 0

Formulate a system of inequalities to represent the given situation about passengers and maintenance costs.

Step-by-step solution

Define variables based on the problem statement.

Formulate the inequality for the total maintenance cost.

Formulate the inequality for the total number of passengers.

Formulate non-negativity inequalities.

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