Every inch on a model is equivalent to 3.5 feet on the real boat. what would be the mathematical...

Question:

Every inch on a model is equivalent to 3.5 feet on the real boat. what would be the mathematical rule to express the relationship between the length of the model, m, and the length of the boat, b?

Ratio and Proportion

Creating mathematical models of real objects involves the process of shrinking or enlarging the original dimensions of the real object with a factor called the scaling factor. This is used in several applications including architecture and engineering

Answer and Explanation:

if the length of the model is represented by m and the length of the boat is represented by b. Their ratio is given by

{eq}m:b = 1\,in:3.5\,ft {/eq}

To answer this, we need to convert the units of measure to inches. We know that {eq}1\,ft=12\,in {/eq} thus the proportion may be rewritten as:

{eq}\begin{align} m:b&=1\,in:3.5\,ft \times \dfrac{12\,in}{1\,ft}\\ m:b&=1:42 \end{align} {/eq}

Since ratios can be converted to fractions, we say that:

{eq}\dfrac{m}{b}=\dfrac{1}{42}\\ {/eq}

We can manipulate this equation and get the relationship between the model m and boat b is given by:

{eq}m=\dfrac{b}{42} {/eq}


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Practice Problems for Calculating Ratios and Proportions

from SAT Prep: Practice & Study Guide

Chapter 30 / Lesson 3
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