The first floor of a house consists of a kitchen, playroom, and dining room. The areas of the kitchen, playroom, and dining room are in the ratio 4:3:2. The combined area of these three rooms is 189 square feet.What is the area of the kitchen?
Accepted Solution
A:
Answer:The area of the kitchen is 84 square feetStep-by-step explanation:Letx-----> the area of the kitchen in square feety ----> the area of the playroom in square feetz ----> the area of the dining room in square feetwe know that[tex]x+y+z=189[/tex] ----> equation A[tex]x:y:z=4:3:2[/tex]so[tex]\frac{x}{y} =\frac{4}{3}[/tex] ----> [tex]y=\frac{3}{4}x[/tex] ---> equation B[tex]\frac{x}{z} =\frac{4}{2}[/tex] ----> [tex]z=\frac{2}{4}x[/tex] ---> equation Csubstitute equation B and equation C in equation A[tex]x+\frac{3}{4}x+\frac{2}{4}x=189[/tex] solve for x[tex]\frac{9}{4}x=189[/tex] [tex]x=189(4)/9\\x=84\ ft^2[/tex]thereforeThe area of the kitchen is 84 square feet