Answer:
The unit rate in feet per inch is 6.32 feet.
Step-by-step explanation:
There are mistakes in questions so the correct question is below:
A blueprint for a house shows the height of the house to be 3 3/8 inches. The actual house is 21 1/3 feet tall. What is the unit rate in feet per inch?
Now, to find the unit rate in feet per inch.
Height of the house in blueprint = [tex]3\frac{3}{8}\ inches=\frac{27}{8}\ inches.[/tex]
The actual height of the house = [tex]21\frac{1}{3}\ feet=\frac{64}{3}\ feet.[/tex]
As:
1 feet = 12 inches.
So, to get the actual height of the house in inches we multiply the actual height of the house by 12:
[tex]\frac{64}{3}\times 12[/tex]
[tex]=\frac{768}{3}[/tex]
[tex]=256\ inches.[/tex]
The actual height of the house in inches = 256 inches.
Now, to get the unit rate in feet we divide the actual height of the house in inches by height of the house in blueprint:
The actual height of the house in inches ÷ Height of the house in blueprint.
[tex]256\ inches\div \frac{27}{8}\ inches[/tex]
As we change the division into multiplication the fraction changes into reciprocal.
= [tex]256\times \frac{8}{27}[/tex]
[tex]=\frac{2048}{27}[/tex]
Now, by using conversion factor:
As, 1 inch = [tex]\frac{1}{12}\ feet[/tex]
So, [tex]\frac{2048}{27}\ inches[/tex]
= [tex]\frac{2048}{27} \times \frac{1}{12}[/tex]
[tex]=\frac{2048}{324} \\=6.32\ feet.[/tex]
Therefore, the unit rate in feet per inch is 6.32 feet.
