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: Determine the scale factor

The scale is 3 in. : 5 ft, so the ratio of blueprint length to actual length is $\frac{3\ \text{in.}}{5\ \text{ft}}$.

Step2: Complete the table

• For 6 in. blueprint length: Since 6 is 2 times 3, actual length is $2\times5 = 10$ ft.
• For 9 in. blueprint length: 9 is 3 times 3, actual length is $3\times5 = 15$ ft.
• For 12 in. blueprint length: 12 is 4 times 3, actual length is $4\times5 = 20$ ft.
• For 15 in. blueprint length: 15 is 5 times 3, actual length is $5\times5 = 25$ ft.
• For 18 in. blueprint length: 18 is 6 times 3, actual length is $6\times5 = 30$ ft.

Step3: Find actual wall length (18 in. blueprint)

From the table, when blueprint length is 18 in., actual length is 30 ft.

Step4: Find blueprint window width (2.5 ft actual)

Let $x$ be blueprint width. Using the scale $\frac{3\ \text{in.}}{5\ \text{ft}}=\frac{x}{2.5\ \text{ft}}$. Cross - multiply: $5x = 3\times2.5$, $5x = 7.5$, $x=\frac{7.5}{5}=1.5$ in.

Answer:

• Table completion (actual lengths): 10, 15, 20, 25, 30 (corresponding to 6, 9, 12, 15, 18 in. blueprint lengths)
• Actual wall length: 30
• Blueprint window width: 1.5