Answer:
[tex]\frac{9}{32}[/tex]
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 = [tex]\frac{3}{10}(5k)=\frac{3}{2}k[/tex]
Number of white squares = [tex]\frac{7}{10}(5k)=\frac{7}{2}k[/tex]
As ratio of black circles to black squares is 3:8,
Number of black circles = [tex]\frac{3}{11} (11k)=3k[/tex]
Number of black squares = [tex]\frac{8}{11}(11k)=8k[/tex]
Total number of circles = [tex]\frac{3}{2}k+3k=\frac{9}{2} k[/tex]
Total number of shapes = [tex]5k+11k=16k[/tex]
Therefore,
Fraction of circles [tex]=\frac{\frac{9}{2} k}{16k} =\frac{9}{32}[/tex]
