Question

A class project requires students to build models of important landmarks around the United States. Teresa and Scott created a 25 in. tall model of the Empire State Building. The actual Empire State Building is 1,250 ft. tall (base to roof). They want to maintain the same scale on their next landmark. How tall would their model of Mount Rushmore be if the actual height of Mount Rushmore is 500 ft.?

Answer 1

Ответ:

To maintain the same scale, we need to calculate the ratio of the height of the model to the actual height of the Empire State Building, and then apply that ratio to the actual height of Mount Rushmore to find the height of the model of Mount Rushmore.

The ratio of the height of the model of the Empire State Building to the actual height of the Empire State Building is:

25 in. / 1,250 ft. = 0.02 in./ft.

To find the height of the model of Mount Rushmore, we can multiply the actual height of Mount Rushmore by this ratio:

Height of model of Mount Rushmore = Actual height of Mount Rushmore x Ratio

Height of model of Mount Rushmore = 500 ft. x 0.02 in./ft.

Height of model of Mount Rushmore = 10 in.

Therefore, Teresa and Scott's model of Mount Rushmore would be 10 inches tall if they maintain the same scale they used for the Empire State Building model.

Answer 2

To maintain the same scale as their Empire State Building model, we can set up a proportion to find the height of their model of Mount Rushmore.

The ratio of the height of their Empire State Building model to the actual height of the Empire State Building is:

Model height of Empire State Building / Actual height of Empire State Building = Model height of Mount Rushmore / Actual height of Mount Rushmore

Let's calculate the model height of Mount Rushmore:

Model height of Mount Rushmore = (Model height of Empire State Building / Actual height of Empire State Building) * Actual height of Mount Rushmore

Substituting the given values:

Model height of Mount Rushmore = (25 in. / 1250 ft.) * 500 ft.

Now, let's convert the inches to feet for consistent units:

1 inch = 1/12 feet

Model height of Mount Rushmore = (25 in. / 1250 ft.) * 500 ft. * (1 ft. / 12 in.)

Simplifying the equation:

Model height of Mount Rushmore = (25 / 1250) * 500 * (1 / 12) feet

Model height of Mount Rushmore = (1 / 50) * 500 * (1 / 12) feet

Model height of Mount Rushmore = (1 * 500 * 1) / (50 * 12) feet

Model height of Mount Rushmore = 500 / 600 feet

Model height of Mount Rushmore ≈ 0.8333 ft.

Therefore, their model of Mount Rushmore would be approximately 0.8333 feet tall.