Alloy

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

Correct answer:

r =  9:35

Step-by-step explanation:

k1 = 1+21 m1 + 2+32 m2 k2 = 1+22 m1 + 2+33 m2  k1 = 31 m1 + 52 m2 k2 = 32 m1 + 53 m2  k1/k2 = 17:27 r = m1/m2  17/27 =  32 m1 + 53 m231 m1 + 52 m2  17 (32 m1 + 53 m2) = 27   (31 m1 + 52 m2) 17 (32 r + 53) = 27   (31 r + 52)  r=17 3227 3127 5217 53=3590.2571   Verifying Solution:  m1=9 kg m2=m1/r=9/359=9:359=9 935=99 35=9315=35 kg  k1=31 m1+52 m2=31 9+52 35=17 kg k2=32 m1+53 m2=32 9+53 35=27 kg  t2=k1/k2=17/27=27170.6296



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