On a set of blueprints for a new home, the contractor has established a scale of 0.5in : 10 ft. what are the dimensions on the blueprints of a bedroom that will be 18 feet by 16 feet.

The dimensions on the blueprints are 0.9 inches and 0.8 inches

Step-by-step explanation:

* Lets explain the relation between the drawing dimensions and

 the real dimensions

- A scale drawing make a real object with accurate sizes reduced

 or enlarged by a certain amount called the scale

- Ex: If the scale drawing is 1 : 10, so anything drawn with the size of

 1 have a size of 10 in the real so a measurement of 15 cm on the

 drawing will be 150 cm on the real

- In a scale drawing, all dimensions have been reduced by the same

 proportion

* Lets solve the problem

- On a set of blueprints for a new home, the contractor has

  established a scale of 0.5 in : 10 ft

∵ The drawing scale ratio must be in same unit

∴ Change the feet to inch

∵ 1 foot = 12 inches

∴ 10 feet = 10 × 12 = 120 inches

∴ The scale is 0.5 inches : 120 inches

- Simplify the scale by multiply it by 2

∴ The scale is 1 in : 240 in

- Lets find the dimensions on the blueprints

∵ The real dimensions are 18 feet and 16 feet

- Change the feet to inches

∴ 18 feet = 18 × 12 = 216 inches

∵ 16 feet = 16 × 12 = 192 inches

∵ The scale is 1 : 240

∴ 1/240 = x/216 ⇒ use cross multiplication

∴ 240 x = 216 divide both sides by 240

∴ x = 0.9 inch

∵ The scale is 1 : 240

∴ 1/240 = y/192 ⇒ use cross multiplication

∴ 240 y = 192 divide both sides by 240

∴ y = 0.8 inch

* The dimensions on the blueprints are 0.9 inches and 0.8 inches