An architect built a model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sports stadium is 180 feet. What is the height of the scale mod... An architect built a model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sports stadium is 180 feet. What is the height of the scale model in inches?

Understand the Problem

The question asks us to find the height of a scale model of a sports stadium given the scale and the actual height of the stadium. We need to use the given scale (2 inches represents 30 feet) to determine how many inches on the model correspond to 180 feet in reality.

Answer

12 inches
Answer for screen readers

12 inches

Steps to Solve

  1. Determine the scale factor.

We are given that 2 inches on the model represents 30 feet in reality. We can write this as a ratio: $$ \frac{2 \text{ inches}}{30 \text{ feet}} $$

  1. Simplify the scale factor.

We can simplify the ratio by dividing both the numerator and denominator by 2: $$ \frac{2 \div 2 \text{ inches}}{30 \div 2 \text{ feet}} = \frac{1 \text{ inch}}{15 \text{ feet}} $$ This means 1 inch on the model represents 15 feet in reality.

  1. Set up a proportion to find the height of the model.

Let $x$ be the height of the model in inches that represents 180 feet. We can set up the proportion: $$ \frac{1 \text{ inch}}{15 \text{ feet}} = \frac{x \text{ inches}}{180 \text{ feet}} $$

  1. Solve for $x$.

To solve for $x$, we can cross-multiply: $$ 1 \cdot 180 = 15 \cdot x $$ $$ 180 = 15x $$ Divide both sides by 15: $$ x = \frac{180}{15} $$ $$ x = 12 $$ Therefore, the height of the scale model is 12 inches.

12 inches

More Information

The scale model is 12 inches tall, which corresponds to 180 feet in the real world. This was calculated using proportions based on the given scale.

Tips

A common mistake would be to incorrectly set up the proportion, for example, inverting the fractions or not using the same units on both sides of the equation. Another error might be to not simplify the initial scale factor, which can make the calculations more difficult, but won't affect the answer if performed correctly.

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