Question

1. when the scale is set to 1:600, a model of the empire state building is 25 inches tall.

a. how tall is a model at a 1:500 scale?

Explanation:

Step1: Find the actual height of the Empire State Building

Let the actual height be \(x\) inches. Given the scale \(1:600\) and model height \(25\) inches.
Since scale \(=\frac{\text{model height}}{\text{actual height}}\), we have \(\frac{1}{600}=\frac{25}{x}\).
Cross - multiply: \(x = 25\times600=15000\) inches.

Step2: Find the model height at \(1:500\) scale

Let the model height at \(1:500\) scale be \(y\) inches.
Using the scale formula \(\frac{1}{500}=\frac{y}{15000}\).
Cross - multiply: \(y=\frac{15000}{500}=30\) inches.

Answer:

The height of the model at a \(1:500\) scale is \(30\) inches.