Potter Lynch
04/24/2024 · Junior High School
Write the scale and write the given corresponding information under the correct ratio. DO NOT SOLVE Kevin bought a \( 7 \frac{2}{3} \) inches tall model of the Statue of Liberty. The scale used for the model was \( \frac{2}{3} \) inch = 4 meters. What is the actual height, in meters, of the Statue of Liberty? Explain how you solved the question.
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Tutor-Verified Answer
Step-by-step Solution
To organize the information given in the problem, we can set up the scale and the corresponding ratios as follows:
**Scale:**
\[
\frac{2}{3} \text{ inch} = 4 \text{ meters}
\]
**Model Height:**
\[
7 \frac{2}{3} \text{ inches}
\]
**Corresponding Ratio:**
To find the actual height of the Statue of Liberty, we will use the scale to set up a proportion based on the model height.
1. Convert the model height to an improper fraction:
\[
7 \frac{2}{3} = \frac{23}{3} \text{ inches}
\]
2. Set up the ratio using the scale:
\[
\frac{\text{Model Height}}{\text{Actual Height}} = \frac{\frac{2}{3} \text{ inch}}{4 \text{ meters}}
\]
3. The actual height can be represented as \( x \) meters, leading to the proportion:
\[
\frac{\frac{23}{3} \text{ inches}}{x \text{ meters}} = \frac{\frac{2}{3} \text{ inch}}{4 \text{ meters}}
\]
This sets up the framework to solve for the actual height \( x \) of the Statue of Liberty, but as per your request, we will not solve it.
Quick Answer
Scale: \( \frac{2}{3} \text{ inch} = 4 \text{ meters} \)
Model Height: \( 7 \frac{2}{3} \text{ inches} \)
Corresponding Ratio: \( \frac{\frac{23}{3} \text{ inches}}{x \text{ meters}} = \frac{\frac{2}{3} \text{ inch}}{4 \text{ meters}} \)
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