Lorenzo's model train is 1/87 the size of the original train. He measures the engine of the model train and finds that it is 2.5 inches tall. What is the height of the real engine to the nearest foot?
Multiply 2.5 inches by 87, convert that number of inches to feet, and round off the answer
18ft
18
To find the height of the real engine, we need to use the scale factor given, which is 1/87.
First, we'll calculate the ratio of the height of the model train engine to the height of the real engine:
Model train engine height / Real engine height = Scale factor
Let's represent the height of the model train engine as "M" and the height of the real engine as "R". From the given information, we know the model train engine height is 2.5 inches:
M = 2.5 inches
Now we can set up the ratio equation:
2.5 inches / R = 1/87
To isolate R, the height of the real engine, we'll cross-multiply and solve for R:
2.5 inches * 87 = R
R ≈ 217.5 inches
Since the question asks for the height of the real engine to the nearest foot, we can convert inches to feet by dividing by 12:
217.5 inches / 12 = 18.125 feet
Rounded to the nearest foot, the height of the real engine is approximately 18 feet.