# A model of the Cape Hatteras Lighthouse uses a scale of 8 inches 30 feet. If the actual lighthouse is 210 feet tall, how tall is the model?

May 27, 2017

#### Answer:

The scale model is $56 \text{ inches}$ tall.

#### Explanation:

Strategy: Use the fact that $8$ inches = $30$ feet as a conversion factor to scale $210$ foot tower to scale model size.

Step 1. Conversion factor.

$8 \text{ inches"=30" feet}$ can be turned into a conversion factor in one of two ways:

$\left(8 \text{ inches")/(30" feet}\right)$ or $\left(30 \text{ feet")/(8" inches}\right)$

Step 2. Scale the $210$ feet by the conversion factor which cancels feet and keeps inches.

210cancel(" feet")xx(8" inches")/(30cancel(" feet"))=56" inches"