Answer :
To solve this problem, we need to find the equation that Howard can use to determine the height of the actual Statue of Liberty in meters, based on his scale model.
We know:
- The height of the model is 15 inches.
- The scale ratio is 1 inch to 6.2 meters.
In a scale model, the relationship between the model size and the actual size is given by multiplying the model size by the scale ratio. So, if 1 inch on the model represents 6.2 meters in real life, the total height of the actual statue (in meters) would be the height of the model multiplied by the scale ratio.
The task is to determine which equation correctly represents this relationship.
1. Let's denote the actual height of the Statue of Liberty in meters as [tex]\( x \)[/tex].
2. According to the scale, 1 inch on the model is equivalent to 6.2 meters of the actual statue.
3. Therefore, for 15 inches on the model, the actual height [tex]\( x \)[/tex] can be found by:
- [tex]\( 15 \times 6.2 = x \)[/tex]
This rearranges to the equation:
- [tex]\( x = 15 \times 6.2 \)[/tex]
Now, let's look at the answer choices to see which equation matches our setup.
A) [tex]\( 15x = 6.2 \)[/tex]
- This implies multiplying 15 by [tex]\( x \)[/tex], which doesn't match our setup.
B) [tex]\( 6.2x = 15 \)[/tex]
- This implies multiplying 6.2 by [tex]\( x \)[/tex], which doesn't match our setup.
C) [tex]\( \frac{1}{6.2} = \frac{x}{15} \)[/tex]
- This setup doesn't properly relate the model height to the actual height.
D) [tex]\( \frac{1}{6.2} = \frac{15}{x} \)[/tex]
- This implies that 1 inch is to 6.2 meters as 15 inches is to [tex]\( x \)[/tex], which rearranges to [tex]\( x = 15 \times 6.2 \)[/tex].
Thus, the correct equation that Howard can use to determine [tex]\( x \)[/tex], the height in meters of the Statue of Liberty, is represented by:
- Equation [tex]\( D: \frac{1}{6.2} = \frac{15}{x} \)[/tex]
After solving, [tex]\( x \)[/tex] equals 93.0 meters.
We know:
- The height of the model is 15 inches.
- The scale ratio is 1 inch to 6.2 meters.
In a scale model, the relationship between the model size and the actual size is given by multiplying the model size by the scale ratio. So, if 1 inch on the model represents 6.2 meters in real life, the total height of the actual statue (in meters) would be the height of the model multiplied by the scale ratio.
The task is to determine which equation correctly represents this relationship.
1. Let's denote the actual height of the Statue of Liberty in meters as [tex]\( x \)[/tex].
2. According to the scale, 1 inch on the model is equivalent to 6.2 meters of the actual statue.
3. Therefore, for 15 inches on the model, the actual height [tex]\( x \)[/tex] can be found by:
- [tex]\( 15 \times 6.2 = x \)[/tex]
This rearranges to the equation:
- [tex]\( x = 15 \times 6.2 \)[/tex]
Now, let's look at the answer choices to see which equation matches our setup.
A) [tex]\( 15x = 6.2 \)[/tex]
- This implies multiplying 15 by [tex]\( x \)[/tex], which doesn't match our setup.
B) [tex]\( 6.2x = 15 \)[/tex]
- This implies multiplying 6.2 by [tex]\( x \)[/tex], which doesn't match our setup.
C) [tex]\( \frac{1}{6.2} = \frac{x}{15} \)[/tex]
- This setup doesn't properly relate the model height to the actual height.
D) [tex]\( \frac{1}{6.2} = \frac{15}{x} \)[/tex]
- This implies that 1 inch is to 6.2 meters as 15 inches is to [tex]\( x \)[/tex], which rearranges to [tex]\( x = 15 \times 6.2 \)[/tex].
Thus, the correct equation that Howard can use to determine [tex]\( x \)[/tex], the height in meters of the Statue of Liberty, is represented by:
- Equation [tex]\( D: \frac{1}{6.2} = \frac{15}{x} \)[/tex]
After solving, [tex]\( x \)[/tex] equals 93.0 meters.
