Question

The table compares actual lengths in a room to lengths in a blueprint of the room. Blueprint length (in.) 6 12 18 24 30 36 Actual length (ft) 7 14 21 28 35 42 Complete the equation for the relationship, where y is the actual length in feet, and x is the blueprint length in inches y = The length of a wall on the blueprint is 10 inches. Find the actual length of the wall. feet long A window in the room has an actual width of 3.5 feet. Find the width of the window in the blueprint. The width of the window in the blueprint is The actual wall is in.​

Answer 1

The relationship between blueprint length and actual length is y = (7/6)x, where y is the actual length in feet and x is the blueprint length in inches. The actual length for a 10-inch blueprint length is 11.67 feet. A window with an actual width of 3.5 feet would be 3 inches wide on the blueprint.

Step-by-step explanation:

From the data provided, we deduce that for every 1 inch on the blueprint, it corresponds to 7 feet in actual length. This can be written as a ratio or a scale factor: 1 inch / 7 feet. Since the ratios must be equivalent, we can set up the proportion for the given blueprint lengths and actual lengths to find the equation of the relationship.

Using the provided data:
Blueprint length of 6 inches corresponds to 7 feet in actual length.
Blueprint length of 12 inches corresponds to 14 feet in actual length, and so on.

Writing this in terms of y (actual length in feet) and x (blueprint length in inches), we get y = (7/6)x.

To find the actual length of the wall on the blueprint that is 10 inches long, we can use this equation:
Actual length y = (7/6) * 10 inches = 11.67 feet.

For the window that has an actual width of 3.5 feet, using the inverse operation, we get:
Blueprint width x = (6/7) * 3.5 feet = 3 inches.