Question

a blueprint for a house shows the height of the house to be $3\frac{1}{8}$ inches. the actual house is $21\frac{1}{3}$ feet tall. what is the unit rate in feet per inch?\
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\\(\bigcirc\\) a. $\frac{75}{512}$ foot per inch\
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\\(\bigcirc\\) b. $6\frac{62}{75}$ feet per inch\
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\\(\bigcirc\\) c. $2\frac{14}{25}$ feet per inch\
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\\(\bigcirc\\) d. $\frac{25}{512}$ foot per inch

Explanation:

Step1: Convert mixed numbers to improper fractions

Blueprint height: $3\frac{1}{8} = \frac{3\times8 +1}{8} = \frac{25}{8}$ inches.
Actual height: $21\frac{1}{3} = \frac{21\times3 +1}{3} = \frac{64}{3}$ feet.

Step2: Calculate unit rate

Divide actual height by blueprint height:
$$\text{Unit rate} = \frac{\frac{64}{3}}{\frac{25}{8}} = \frac{64}{3} \times \frac{8}{25} = \frac{512}{75}$$

Step3: Convert back to mixed number

$\frac{512}{75}=6\frac{62}{75}$

Answer:

B. $6\frac{62}{75}$ feet per inch