Busi has

Busi has a bag containing twenty balls. There are twice as many yellow balls as blue balls, but the yellow balls are only a third of the red balls. The green balls are the same number as the blue balls. How many are each color ball?

Correct answer:

y =  4
r =  12
b =  2
g =  2

Step-by-step explanation:

$$\begin{gathered} y=2b \\ y=r/3 \\ g=b \\ y+b+r+g=20 \\ y=2\cdot b \\ y=r/3 \\ g=b \\ y+b+r+g=20 \\ 2b-y=0 \\ r-3y=0 \\ b-g=0 \\ b+g+r+y=20 \\ Row3-\frac{1}{2}\cdot Row1\to Row3 \\ 2b-y=0 \\ r-3y=0 \\ -g+0.5y=0 \\ b+g+r+y=20 \\ Row4-\frac{1}{2}\cdot Row1\to Row4 \\ 2b-y=0 \\ r-3y=0 \\ -g+0.5y=0 \\ g+r+1.5y=20 \\ Pivot:Row2\leftrightarrow Row3 \\ 2b-y=0 \\ -g+0.5y=0 \\ r-3y=0 \\ g+r+1.5y=20 \\ Row4+Row2\to Row4 \\ 2b-y=0 \\ -g+0.5y=0 \\ r-3y=0 \\ r+2y=20 \\ Row4-Row3\to Row4 \\ 2b-y=0 \\ -g+0.5y=0 \\ r-3y=0 \\ 5y=20 \\ y=\frac{20}{5}=4 \\ r=0+3y=0+3\cdot 4=12 \\ g=\frac{0-0.5y}{-1}=\frac{0-0.5\cdot 4}{-1}=2 \\ b=\frac{0+y}{2}=\frac{0+4}{2}=2 \\ b=2 \\ g=2 \\ r=12 \\ y=4 \end{gathered}$$

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