Question

white shapes and black shapes are used in a game. some of the shapes are circles all the other shapes are squares.
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 are circles. :)

Answer 1

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$

fraction of all the shapes are circles=9/32

$\huge\red{\underbrace{\overbrace{\ulcorner{\mid{\overline{\underline{EXPLANATION}}}}}}}$

${\bf{\red{Find the equivalent ratio for the total shapes:}}}$

${\bf{\green{total Black shapes: total white shapes}}}$

${\bf{\green{=>5:11}}}$

${\bf{\green{multiple by 2:}}}$

${\bf{\green{=>10:22}}}$

${\bf{\green{Ratio of the white shapes:}}}$

${\bf{\green{White circles : white squares}}}$

${\bf{\green{=>3:7}}}$

${\bf{\green{sum of the units=3+7=>10}}}$

${\bf{\pink{Find the equivalent ratio for the total shapes:}}}$

${\bf{\blue{Black circles : Black squares }}}$

${\bf{\blue{=>3:8}}}$

${\bf{\blue{Multiple by 2:}}}$

${\bf{\blue{=>6:16}}}$

${\bf{\blue{sum of the units=6+16=>22}}}$

${\bf{\green{Now combine the total ratios:}}}$

${\bf{\orange{(white)circles:squares:(black)circles:squares}}}$

${\bf{\orange{=>3:7:6:16}}}$

${\bf{\orange{circles=3+6=>9 units}}}$

${\bf{\orange{Total=3+7+6+16}}}$

${\bf{\orange{Total=32 units}}}$

${\bf{\blue{The fraction of all the shapes that are circles:}}}$

${\bf{\red{Fraction=9/32}}}$

Answer 2

Find the equivalent ratio for the total shapes:

Total Black Shapes : Total White Shapes = 5 : 11

Multiply by 2:

Total Black Shapes: Total White Shapes = 10 : 22

Find the ratio for the white shapes:

White circles : White squares = 3 : 7

Sum of the units = 3 + 7

Sum of the units = 10

Find the equivalent ratio for the total shapes:

Black circles : Black squares = 3 : 8

Multiply by 2:

Black circles : Black squares = 6 : 16

Sum of the units = 6 + 16

Sum of the units = 22

Combine the ratios:

white circles : white squares : black circles : black square = 3 : 7 : 6 : 16

Circles = 3 + 6

Circles = 9 units

Total = 3 + 7 + 6 + 16

Total = 32 units

Find the fraction of all the shapes that are circles:

Fraction = 9/32