A model of a skyscraper is made using a scale of 1 inch: 75 feet. What is the height of the actual building if the height of the model is 19 2/5?

To find the height of the actual building based on the scale model, you need to multiply the height of the model by the scale ratio.

The given scale is \( 1 \text{ inch} : 75 \text{ feet} \), meaning for every 1 inch of the model, the actual building is 75 feet tall.

The height of the model is given as \( 19 \frac{2}{5} \text{ inches} \).

### Step-by-step solution:
1. Convert the mixed number \( 19 \frac{2}{5} \) into an improper fraction:
   \[
   19 \frac{2}{5} = \frac{19 \times 5 + 2}{5} = \frac{95 + 2}{5} = \frac{97}{5}
   \]

2. Now, multiply the height of the model by the scale ratio:
   \[
   \text{Height of actual building} = \frac{97}{5} \times 75
   \]

3. Simplify the multiplication:
   \[
   \frac{97}{5} \times 75 = \frac{97 \times 75}{5} = \frac{7275}{5} = 1455 \text{ feet}
   \]

So, the actual height of the building is **1455 feet**.

Would you like any additional details or clarifications?

Here are some related questions:
1. What would be the height of the model if the actual building were 1200 feet tall?
2. If the scale were changed to 1 inch: 100 feet, what would the new model height be for the same building?
3. How do you calculate the actual dimensions of a building when given a model's length and width?
4. If another model uses a scale of 1 inch: 50 feet, how would this affect the model's height compared to the original?
5. How can we convert between different scale units, such as meters instead of feet?

**Tip:** Always ensure that the scale units match when making comparisons between model dimensions and actual dimensions.

Find the height of an actual skyscraper given a scale model with a ratio of 1 inch: 75 feet and a model height of 19 2/5 inches. This problem uses proportions and mixed number conversions to calculate the actual building height of 1455 feet. Suitable for middle school students in Grades 6-8.

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