SOLUTION: Tia and Lamar are making a scale model of a lighthouse. The actual lighthouse is 175 feet high. The scale for the model is 4 feet : 1/2 inch. How tall should their scale model be?

Question 885477: Tia and Lamar are making a scale model of a lighthouse. The actual lighthouse is 175 feet high. The scale for the model is 4 feet : 1/2 inch. How tall should their scale model be?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
lighthouse is 175 feet high.
scale model is 4 feet : 1/2 inch.
this means that every half inch is equal to 4 feet.
you set up a ratio:
175 / x = 4 / (1/2)
this ratio means:
175 feet is to x inches as 4 feet is to 1/2 inch.
you can cross multiply to solve, but we'll do it a different, but equivalent, way.
4 / (1/2) is equal to 8, so your equation becomes:
175 / x = 8
multiply both sides of this equation by x and divide both sides of this equation by 8 to get:
175 / 8 = x
simplify to get:
x = 21.875 inches.

your scale model should be 21.875 inches high.
since each 1/2 inch represents 4 feet, this means that each inch represents 8 feet and 21.875 * 8 = 175 feet which means the scale is correct.
21.875 inches is the same as 21 and 7/8 inches.

if you had cross multiplied you would have gotten the following:
175/x = 4/(1/2)
cross multiply to get:
4x = (1/2)*175
divide both sides of this equation by 4 to get:
x = (1/2) * 175 / 4 which becomes:
x = 175 / 8 which becomes:
x = 21.875

another way to look at it.
your lighthouse is 175 feet high.
the scale is 4 feet for every 1/2 inch.
divide 175 by 4 to get 43.75
this means that the scale model is equal to 43.75 half inch segments.
43.75 half inch segments is equal to 21.875 full inch segments.
the height of the tower is modeled by 21.875 inches in height.

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