Respuesta :
Given:
A model of a famous statue is [tex]3\dfrac{1}{2}[/tex] inches tall. The actual statue is [tex]5\dfrac{1}{4}[/tex] feet tall.
To find:
The the ratio of the height of the model to the height of the actual statue in simplest form.
Solution:
We have,
Height of the model = [tex]3\dfrac{1}{2}[/tex] inches
Height of the actual statue = [tex]5\dfrac{1}{4}[/tex] feet.
Now, the ratio of the height of the model to the height of the actual statue is:
[tex]\text{Ratio}=\dfrac{\text{Height of model}}{\text{Height of actual statue}}[/tex]
[tex]\text{Ratio}=\dfrac{3\dfrac{1}{2}\ in.}{5\dfrac{1}{4}\ ft}[/tex]
[tex]\text{Ratio}=\dfrac{\dfrac{3(2)+1}{2}\ in.}{\dfrac{5(4)+1}{4}\ ft}[/tex]
[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{\dfrac{21}{4}\ ft}[/tex]
We know that 1 ft = 12 in.
[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{\dfrac{21}{4}\times 12\ in.}[/tex]
[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{21\times 3\ in.}[/tex]
[tex]\text{Ratio}=\dfrac{7}{2\times 21\times 3}[/tex]
[tex]\text{Ratio}=\dfrac{1}{2\times 3\times 3}[/tex]
[tex]\text{Ratio}=\dfrac{1}{18}[/tex]
Therefore, the ratio of the height of the model to the height of the actual statue in simplest form is [tex]\dfrac{1}{18}[/tex].
