(cashews/beetroots) 66984

The lady sells nuts. It has two mixtures of nuts (cashews/beetroots) in a ratio of 2:1 and 1:3 (cashews and peanuts). Determine the ratio to mix both mixtures so that the ratio of cashews/beetroot in the resulting mixture is 1:2.
(Please provide a certificate on which principle this is calculated)

Correct answer:

r =  1:4

Step-by-step explanation:

s1: k:b=2:1 = 2x:1x s2: k:b=1:3 = 1y:3y  s1: k = 2b s2: k = b/3  k:b = 1:2  x=1  k=2 x+1 y b=1 x+3 y k=b/2 k=2 1+1 y b=1 1+3 y k=b/2  ky=2 b3y=1 b2k=0  Pivot:Row1Row2 b3y=1 ky=2 b2k=0  Row3Row1Row3 b3y=1 ky=2 2k+3y=1  Pivot:Row2Row3 b3y=1 2k+3y=1 ky=2  Row321 Row2Row3 b3y=1 2k+3y=1 0.5y=1.5  y=0.51.5=3 k=213y=213 3=5 b=1+3y=1+3 3=10  b=10 k=5 y=3  r=1 y+3 y2 x+1 x=1 3+3 32 1+1 1=41=0.25=1:4

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