# 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?

Result

x =  0.33

#### Solution:

$\dfrac{a+b}{c+d} = \dfrac{5}{3} \ \\ \dfrac{a}{b} = \dfrac{1}{2} \ \\ \dfrac{c}{d} = \dfrac{1}{8} \ \\ \ \\ a = 1 \ \\ b = 2 \ \\ c = 0.2 \ \\ d = 1.6 \ \\ \ \\ x = \dfrac{ a+b }{c+d} = 0.33 = 1/3 \ \\$

a=1
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 = 15 = 0.2
d = 85 = 1.6

Calculated by our linear equations calculator.

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