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

Answer:

Part a) The scale of the new blueprint is $\frac{5}{8} \frac{in}{ft}$    

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

Step-by-step explanation:

we know that

The scale of the original blueprint is

$\frac{2}{5}\frac{in}{ft}$

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

$\frac{2}{5}\frac{in}{ft}=\frac{6}{x}\frac{in}{ft}\\ \\x=5*6/2\\ \\x=15\ ft$

Find the actual length of the living room, using proportion

$\frac{2}{5}\frac{in}{ft}=\frac{9.6}{x}\frac{in}{ft}\\ \\x=5*9.6/2\\ \\x=24\ ft$

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

$\frac{15}{24} \frac{in}{ft}$

simplify  

$\frac{5}{8} \frac{in}{ft}$      

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

$\frac{5}{8}\frac{in}{ft}=\frac{x}{15}\frac{in}{ft}\\ \\x=15*5/8\\ \\x=9.4\ in$