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The square is divided into 4 parts, W, X, Y and Z. W and X form 1/2 of the square. The area of Y is double of the area of Z, while the ratio of the area of X to the area of W is 1:3. What fraction of the square is the sum of the area of X and Y? Leave the answer(s) in the simplest form.

 Mar 28, 2022
 #1
avatar+122385 
+2

Since W and X  form 1/2 of the area, then   Z and Y  form the other half

 

So  

 

Z + Y   =    1/2        and     (1/2)Y + Y  =  1/2    .....so.....

 

(3/2)Y  = 1/2

 

Y  =  (1/2) ( 2/3)  =   1/3

 

And

 

W + X =   1/2    and    3X + X  = 1/2   .....so....

 

4X  = 1/2

 

X =  (1/2) (1/4)  =   1/8

 

So

 

X + Y  =    (1/8)  + ( 1/3)  =    11/24

 

 

cool cool cool

 Mar 29, 2022
edited by CPhill  Mar 29, 2022
 #2
avatar+138 
+2

w + x = 1/2

w + x + y + z = 1

y + z = 1 - (w + x)

y + z = 1 - 1/2

y + z = 1/2

 

y = 2z

2z + z = 1/2

3z + 1/2

z = 1/6

y + 1/6 = 1/2
y = 1/2 - 1/6

y = 1/3

 

 

 

x/w = 1/3

3x = w

w + x = 1/2

3x + x = 1/2

4x = 1/2

x = 1/8

x + y = 1/8 + 1/3 = 11/24

 Apr 2, 2022

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