Answer:
The fraction of all shapes which are square in shape is
.
Step-by-step explanation:
Given that , in a game , white and black shapes are used. Some of them are circle in shape and remains are square in shape.
The ratio of white to black shapes are 5:11.
Consider 5x= the number of shapes which are white in color.
11x= The number of shapes which are black in color.
There are (5x+11x)= 16x shapes in the game.
The white circle and white square are in the ratio 3:7.
The number of white square is
![=(\textrm{The number of white shape})\times (\frac{7}{3+7})](https://tex.z-dn.net/?f=%3D%28%5Ctextrm%7BThe%20number%20of%20white%20shape%7D%29%5Ctimes%20%28%5Cfrac%7B7%7D%7B3%2B7%7D%29)
![=(5x)\times (\frac{7}{10})](https://tex.z-dn.net/?f=%3D%285x%29%5Ctimes%20%28%5Cfrac%7B7%7D%7B10%7D%29)
![=\frac{7x}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7x%7D%7B2%7D)
The black circles and black square are in the ratio 3:8
The number of black square is
![=(\textrm{The number of black shape})\times (\frac{8}{3+8})](https://tex.z-dn.net/?f=%3D%28%5Ctextrm%7BThe%20number%20of%20black%20shape%7D%29%5Ctimes%20%28%5Cfrac%7B8%7D%7B3%2B8%7D%29)
![=(11x)\times (\frac{8}{11})](https://tex.z-dn.net/?f=%3D%2811x%29%5Ctimes%20%28%5Cfrac%7B8%7D%7B11%7D%29)
=8x
Therefore the total number of shape which are square is
![=\frac{7x}{2}+8x](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7x%7D%7B2%7D%2B8x)
![=\frac{7x+16x}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7x%2B16x%7D%7B2%7D)
![=\frac{23x}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B23x%7D%7B2%7D)
The fraction of all shape are square is
![=\frac{\textrm{shape in square}}{\textrm{Total number shape}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctextrm%7Bshape%20in%20square%7D%7D%7B%5Ctextrm%7BTotal%20number%20shape%7D%7D)
![=\frac{\frac{23x}{2}}{16x}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cfrac%7B23x%7D%7B2%7D%7D%7B16x%7D)
![=\frac{23}{32}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B23%7D%7B32%7D)