Final answer:
The scale of the drawing that Luca made is 1 inch on the drawing represents 30 inches in real life, or a scale factor of 1:30.
Step-by-step explanation:
To determine the scale of the drawing that Luca made, we can set up a proportion comparing the real-life size to the scale size. Since the real life stage is 45 feet long and the drawing shows it as 18 inches long, we first need to ensure both measures are in the same units. There are 12 inches in a foot, so the stage is 45 feet x 12 inches/foot = 540 inches in real life.
To find the scale, we divide the drawing length by the real length: 18 inches (drawing) ÷ 540 inches (real) = 1/30. This means that the scale of the drawing is 1 inch on the drawing represents 30 inches in real life, or equivalently, 1 inch:30 inches or 1:30 when expressed as a scale factor.