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

Answer:

$\frac{9}{32}$

Step-by-step 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 = $\frac{3}{10}(5k)=\frac{3}{2}k$

Number of white squares = $\frac{7}{10}(5k)=\frac{7}{2}k$

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

Number of black circles = $\frac{3}{11} (11k)=3k$

Number of black squares = $\frac{8}{11}(11k)=8k$

Total number of circles = $\frac{3}{2}k+3k=\frac{9}{2} k$

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

Therefore,

Fraction of circles $=\frac{\frac{9}{2} k}{16k} =\frac{9}{32}$