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:

$$\begin{gathered} {\displaystyle \frac{a+b}{c+d}}={\displaystyle \frac{5}{3}} \\ {\displaystyle \frac{a}{b}}={\displaystyle \frac{1}{2}} \\ {\displaystyle \frac{c}{d}}={\displaystyle \frac{1}{8}} \\ a=1 \\ b=2 \\ c=0.2 \\ d=1.6 \\ x={\displaystyle \frac{a+b}{c+d}}=0.33=1\mathrm{/}3 \end{gathered}$$

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 = 1/5 = 0.2
d = 8/5 = 1.6

Our linear equations calculator calculates it.

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