Final answer:
To calculate the length of the stage in the scale drawing with a scale of 8 inches : 5 feet, set up a proportion and solve, which results in the stage being 80 inches long in the drawing.
Step-by-step explanation:
Sean made a scale drawing of the auditorium using the scale 8 inches : 5 feet. To find the length of the stage in the drawing when the actual length of the stage is 50 feet, we can set up a proportion using the given scale factor. The scale factor means that for every 8 inches in the drawing, the actual size is 5 feet. Therefore, we can write the proportion as 8 inches / 5 feet = x inches / 50 feet. To solve for x, which will give us the length of the stage in the drawing, we use cross-multiplication.
Using cross-multiplication:
8 inches * 50 feet = 5 feet * x
400 = 5x
Now divide by 5 to isolate x:
400 / 5 = x
80 = x
Therefore, the length of the stage in the scale drawing is 80 inches.