BW-BS balls

Adam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8

What is the ratio of all black to all white balls?

Correct answer:

x =  0.33

Step-by-step explanation:

a+bc+d=53 ab=12 cd=18  a=1 b=2 c=0.2 d=1.6  x=a+bc+d=0.33=1/3 

a+b = 5/3•(c+d)
a = 1/2•b
c = 1/8 • d

a = 1
3a+3b-5c-5d = 0
2a-b = 0
8c-d = 0

a = 1
b = 2
c = 1/5 = 0.2
d = 8/5 = 1.6

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