Question

1. a scale model of an aircraft carrier uses a scale in which 1 inch represents 500 feet. if the beam of the actual aircraft carrier is 200 feet, what is the length of the beam on the scale model in inches?

Explanation:

Step1: Define the scale ratio

The scale is 1 inch : 500 feet, which means the ratio of model length to actual length is $\frac{1\ \text{inch}}{500\ \text{feet}}$.

Step2: Set up a proportion

Let $x$ be the length of the beam on the scale model in inches. We set up the proportion $\frac{x}{200\ \text{feet}}=\frac{1\ \text{inch}}{500\ \text{feet}}$.

Step3: Solve for $x$

Cross - multiply: $500x = 200\times1$. Then $x=\frac{200}{500}=0.4$.

Answer:

The length of the beam on the scale model is $0.4$ inches.