Question

White and black shapes are used in a game Some of the shapes are circles All the other shapes are squares The ratio of white to black shapes is 5:11 The ration of white circles to white squares is 3:7 The ratio of black circles to black squares is 3:8 What fraction of all the shapes are squares

Answer 1

Answer:

The fraction of all shapes which are square in shape is $\frac{23}{32}$.

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

$=(\textrm{The number of white shape})\times (\frac{7}{3+7})$

$=(5x)\times (\frac{7}{10})$

$=\frac{7x}{2}$

The black circles and black square are in the ratio 3:8

The number of black square is

$=(\textrm{The number of black shape})\times (\frac{8}{3+8})$

$=(11x)\times (\frac{8}{11})$

=8x

Therefore the total number of shape which are square is

$=\frac{7x}{2}+8x$

$=\frac{7x+16x}{2}$

$=\frac{23x}{2}$

The fraction of all shape are square is

$=\frac{\textrm{shape in square}}{\textrm{Total number shape}}$

$=\frac{\frac{23x}{2}}{16x}$

$=\frac{23}{32}$