white shapes and black shapes are used in a game some of the shapes are circles all other shapes are squares the ratio of the number of white shapes to the number of black shapes in 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 in 3:8 work out what fraction of all the shapes are circles
Answers
Circles are 9/32 fraction of all the shapes
Step-by-step explanation:
Ratio of white shapes to the number of black shapes in 5:11
Let say White Shapes = 5S
Then Black Shapes = 11S
Total Shapes = 16S
White Circles = C
White Squares = 5S - C
Black Circle = B
Black Squares = 11S - B
number of white circles to the number of white squares is 3:7
C/(5S - C) = 3/7
=> 7C = 15S - 3C
=> 10C = 15S
=> C = 3S/2
ratio of the number of black circles to the number of black squares in 3:8
=> B/(11S - B) = 3/8
=>8B = 33S - 3B
=> 11B = 33S
=> B = 3S
Total Circles = Black Circles + White Circle = B +C
= 3S + 3S/2
= 9S/2
Total Shapes = 16S
Ratio = (9S 2/(16S) = 9/32
Circles are 9/32 fraction of all the shapes
One Example :
White Shapes 10 , Black Shapes 22 , Total Shapes 32
White Circle = 3 , White Square 7
Black Circles 6 , Black Square 16
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