# Alloy

The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to the same order of the two metals).

Result

k =  0.29

#### Solution:

$\dfrac12 k+\dfrac23=\dfrac{ 17}{27}\cdot (k+1) \ \\ \ \\ k = \dfrac{2}{7} \doteq 0.29$

1/2*k+2/3=17/27*(k+1)

7k = 2

k = 27 ≈ 0.285714

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