Question

White shapes and black shapes are used in a game some are circles some are squares the ratio of white shapes to black shapes is5:11 the ratio of white circles to white squares are 3:7 the ratio of black circles to black squares are 3:8 work out what fraction of all the shapes are circles

Answer 1

`(9)/(32)`

Explanation:

Given:

Ratio of white shapes to black shapes is 5:11

Ratio of white circles to white squares is 3:7

Ratio of black circles to black squares is 3:8

To find: fraction of all the shapes that are circles

Solution:

As ratio of white shapes to black shapes is 5:11,

let number of white shapes be 5 k and number of black shapes by 11 k

As ratio of white circles to white squares is 3:7,

Number of white circles =
`(3)/(10)(5k)=(3)/(2)k`

Number of white squares =
`(7)/(10)(5k)=(7)/(2)k`

As ratio of black circles to black squares is 3:8,

Number of black circles =
`(3)/(11) (11k)=3k`

Number of black squares =
`(8)/(11)(11k)=8k`

Total number of circles =
`(3)/(2)k+3k=(9)/(2) k`

Total number of shapes =
`5k+11k=16k`

Therefore,

Fraction of circles
`=((9)/(2) k)/(16k) =(9)/(32)`