Question

the scale of a room in a blueprint is 3 in. : 5 ft. a wall in the same blueprint is 18 in. complete the table.

blueprint length (in.)	3	6	9	12	15	18
actual length (ft)	5

how long is the actual wall?
the actual wall is feet long.
a window in the room has an actual width of 2.5 feet. find the width of the window in the blueprint.
the width of the window in the blueprint is in.

Explanation:

Step1: Understand the scale

The scale is 3 in. : 5 ft, meaning 3 inches on blueprint = 5 feet actual. So the ratio of blueprint length (in) to actual length (ft) is 3:5, or the actual length for \( x \) inches blueprint is \( \frac{5}{3}x \) ft, and blueprint length for \( y \) ft actual is \( \frac{3}{5}y \) in.

Step2: Complete the table

• For 6 in: Actual length = \( \frac{5}{3} \times 6 = 10 \) ft.
• For 9 in: Actual length = \( \frac{5}{3} \times 9 = 15 \) ft.
• For 12 in: Actual length = \( \frac{5}{3} \times 12 = 20 \) ft.
• For 15 in: Actual length = \( \frac{5}{3} \times 15 = 25 \) ft.
• For 18 in: Actual length = \( \frac{5}{3} \times 18 = 30 \) ft.

Step3: Actual wall length (18 in blueprint)

From above, when blueprint is 18 in, actual is 30 ft.

Step4: Blueprint width for 2.5 ft actual

Using blueprint length = \( \frac{3}{5} \times \) actual length. So \( \frac{3}{5} \times 2.5 = 1.5 \) in.

Answer:

s:

• Table (Actual length for each blueprint length): 10, 15, 20, 25, 30 (for 6,9,12,15,18 in respectively)
• Actual wall length: 30 feet
• Blueprint window width: 1.5 inches