Question

Please help me. The original blueprint of the Moreno’s’ living room has a scale of 2 inches= 5 feet. The family wants to use a new blueprint that shows the length of the living room to be 15 inches. If the width of the living room on the original blueprint is 6 inches and the length is 9.6 inches, what are the scale and the width of the new blueprint.

Answer 1

Part a) The scale of the new blueprint is
`(5)/(8) (in)/(ft)`

Part b) The width of the living room in the new blueprint is
`9.4\ in`

Explanation:

we know that

The scale of the original blueprint is

`(2)/(5)(in)/(ft)`

and

the width of the living room on the original blueprint is 6 inches

so

Find the actual width of the living room, using proportion

`(2)/(5)(in)/(ft)=(6)/(x)(in)/(ft)\\ \\x=5*6/2\\ \\x=15\ ft`

Find the actual length of the living room, using proportion

`(2)/(5)(in)/(ft)=(9.6)/(x)(in)/(ft)\\ \\x=5*9.6/2\\ \\x=24\ ft`

Find the scale of the new blueprint, divide the length of the living room on the new blueprint by the actual length of the living room

`(15)/(24) (in)/(ft)`

simplify

`(5)/(8) (in)/(ft)`

Find the width of the living room in the new blueprint, using proportion

`(5)/(8)(in)/(ft)=(x)/(15)(in)/(ft)\\ \\x=15*5/8\\ \\x=9.4\ in`