Question

A model of a famous statue is 3 1/2 inches tall. The actual statue is 5 1/4 feet tall. What is the ratio of the height of the model to the height of the actual statue in simplest form?

Answer 1

Given:

A model of a famous statue is
`3(1)/(2)` inches tall. The actual statue is
`5(1)/(4)` 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 =
`3(1)/(2)` inches

Height of the actual statue =
`5(1)/(4)` feet.

Now, the ratio of the height of the model to the height of the actual statue is:

`\text{Ratio}=\frac{\text{Height of model}}{\text{Height of actual statue}}`

`\text{Ratio}=(3(1)/(2)\ in.)/(5(1)/(4)\ ft)`

`\text{Ratio}=((3(2)+1)/(2)\ in.)/((5(4)+1)/(4)\ ft)`

`\text{Ratio}=((7)/(2)\ in.)/((21)/(4)\ ft)`

We know that 1 ft = 12 in.

`\text{Ratio}=((7)/(2)\ in.)/((21)/(4)* 12\ in.)`

`\text{Ratio}=((7)/(2)\ in.)/(21* 3\ in.)`

`\text{Ratio}=(7)/(2* 21* 3)`

`\text{Ratio}=(1)/(2* 3* 3)`

`\text{Ratio}=(1)/(18)`

Therefore, the ratio of the height of the model to the height of the actual statue in simplest form is
`(1)/(18)`.