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

9/32

Explanation:

Answer 2

The fraction of all shapes which are square in shape is
`(23)/(32)`.

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})* ((7)/(3+7))`

`=(5x)* ((7)/(10))`

`=(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})* ((8)/(3+8))`

`=(11x)* ((8)/(11))`

=8x

Therefore the total number of shape which are square is

`=(7x)/(2)+8x`

`=(7x+16x)/(2)`

`=(23x)/(2)`

The fraction of all shape are square is

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

`=((23x)/(2))/(16x)`

`=(23)/(32)`