Question

The length of the sofa on the plans is ____"(Simplify your answer. Type an integer, fraction, or mixed number.)

Answer 1

Given:

$\frac{1}{6}^{\doubleprime}\text{ on a plan for 1 foot }$

The length of the sofa is 6'3''.

We need to convert the foot into inches.

$1\text{ foot = 12 inches.}$$1^{\prime}=12^{\doubleprime}$

Multiply both sides by 6, we get

$1\times6^{\prime}=12\times6^{\doubleprime}$

$6^{\prime}=72^{\doubleprime}$

The length of the sofa is

$6^{\prime}3^{\doubleprime}=72^{\doubleprime}+3^{\doubleprime}=75^{\doubleprime}$

The scale of the plan is

$\frac{1}{6}^{\doubleprime}\colon1^{\prime}$

$\frac{1}{6}^{\doubleprime}\colon12^{\doubleprime}$

Multiply by 75/12 on both sides, we get

$\frac{75}{12}\times\frac{1}{6}^{\doubleprime}\colon\frac{75}{12}\times12^{\doubleprime}$

$\frac{75}{72}^{\doubleprime}\colon75^{\doubleprime}$

$1\frac{3}{72}^{\doubleprime}=75^{\doubleprime}$

$1\frac{1}{24}^{\doubleprime}=75^{\doubleprime}$

Hence the length of the sofa on the plan is

$1\frac{1}{24}^{\doubleprime}$