Question

White shapes and black shapes are used in a game some of the shapes are circles all other shapes are sqaures The ratio of the number of white shapes to the number of black shapes is 5:11 The ratio of the number of white circles to the number of white squares is 3:7 The ratio of the number of black circles to the number of black squares is 3:8 work out what fraction of all the shapes is circles

Answer 1

The fraction of all the shapes are circles is
`(9)/(32)`

Explanation:

There are two types of the shapes in a game.

Circle

Square

The ratio of number of white shapes to the number of black shapes is 5 : 11.

Consider there are 50 white shapes and 110 black shapes.

The ratio of the number of white circles to the number of white squares is 3 : 7.

Here 3/10 of the white shapes are circle and 7/10 are white squares.

The number of white circles can be obtained as follows,

White circles = 3/10 × 50

= 50

The number of white squares can be obtained as follows,

White squares = 7/10 × 50

= 35

The number of black circles to the number of black squares is 3/8.

The number of black circles can be obtained as follows,

Black circles = 3/11 × 110

= 30

The number of black squares can be obtained as follows,

Black squares = 8/11 × 110

= 80

The total number of circles is 30 + 15 = 45 and the total number of shapes is 50 + 110 = 160.

The fractions of all the shapes are circles are 45/160 which is simplified to 9/32

The fraction of all the shapes are circles is 9/32