Question

a small plane’s maximum takeoff weight is 2100 pounds or less. six passengers weigh an average of 150 pounds each. 2. use an inequality to find the luggage and cargo weight that the plane can carry. b. explain the meaning of the answer to part a. a. let x represent the weight of the luggage and cargo. the answer is {x | (type an inequality.)} b. explain the meaning of the answer to part a. choose the correct answer below. a. the luggage and cargo must weigh 1200 pounds or less. b. the luggage and cargo must weigh 1950 pounds or less. c. the luggage and cargo must weigh 1950 pounds or more. d. the luggage and cargo must weigh 1200 pounds or more.

Explanation:

Part a:

Step1: Calculate total passenger weight

Six passengers, each averaging 150 pounds, so total passenger weight is \(6\times150 = 900\) pounds.

Step2: Set up inequality for total weight

Let \(x\) be luggage and cargo weight. Total takeoff weight (passengers + luggage + cargo) must be \(\leq2100\) pounds. So \(900 + x\leq2100\).

Step3: Solve the inequality

Subtract 900 from both sides: \(x\leq2100 - 900\), so \(x\leq1200\).

The inequality \(x\leq1200\) means the weight of luggage and cargo (\(x\)) must be 1200 pounds or less. This is because the total takeoff weight (passengers' weight + luggage/cargo weight) can't exceed 2100 pounds. After calculating passengers' total weight (900 pounds), we find the maximum allowable weight for luggage and cargo is 1200 pounds, so \(x\) (their weight) must be at most 1200 pounds.

Answer:

\(x\leq1200\) (or \(\{x\mid x\leq1200\}\))

Part b: