Question

a small plane’s maximum takeoff weight is 1800 pounds or less. six passengers weigh an average of 150 pounds each.
a. 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 | \box}.
(type an inequality.)

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/cargo weight. Total weight (passengers + luggage/cargo) must be ≤ 1800. So \(900 + x \leq 1800\).

Step3: Solve for \(x\)

Subtract 900 from both sides: \(x \leq 1800 - 900\), so \(x \leq 900\).

The inequality \(x \leq 900\) means the weight of luggage and cargo (represented by \(x\)) that the plane can carry must be 900 pounds or less. This is because the total weight of passengers (900 pounds) plus luggage/cargo weight must not exceed the plane’s maximum takeoff weight of 1800 pounds.

Answer:

\(\{x\mid x \leq 900\}\)

Part b