70.1k views
2 votes
A sculptor makes a miniature model before starting the final version. Her model is scaled so that of 1/4 of an inch corresponds to 6 feet on the final version. The base of her model is 5/12 of an inch. How big will the base of the final be?

User Justin Lee
by
8.1k points

1 Answer

6 votes

Answer:

10 feet

Explanation:

To find out the size of the base of the final version, we need to determine the scaling factor between the model and the final version.

Given that 1/4 of an inch on the model corresponds to 6 feet on the final version, we can set up the following proportion:


(1/4 \ in)/( 6 \ ft) = ( 5/12 \ in )/( x )

To solve for x, we cross-multiply:


\Longrightarrow (1/4 \ in)(x)= (5/12 \ in)(6 \ ft)

Now, let's simplify the equation:


\Longrightarrow \Big((1)/(4) \ in\Big)(x )= \Big(\frac52 \ ft \cdot in\Big)

To eliminate the fraction, we can multiply both sides of the equation by 4:


\Longrightarrow \Big((1)/(4) \ in\Big)(x)= \Big(\frac52 \ ft \cdot in\Big)\\\\\\\\\Longrightarrow x= \Big(\frac52 \ ft \cdot in\Big)\Big(4 \ in^(-1) \Big)\\\\\\\\\therefore \boxed{\boxed{x=10 \ ft}}

Therefore, the base of the final version will be 10 feet.

User TheShun
by
8.6k points