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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?

Respuesta :

calculista

Answer:

The area of the kitchen is 84 square feet

Step-by-step explanation:

Let

x-----> the area of the kitchen in square feet

y ---->  the area of the playroom in square feet

z ---->  the area of the dining room in square feet

we 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 C

substitute 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]

therefore

The area of the kitchen is 84 square feet

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