Aparticular metal alloy a has 20% iron and another alloy b contains 60% iron. how many kilograms of each alloy should be combined to create 80 kg of a 52% iron alloy?

Let t and s represent the masses of 20% and 60% alloys respectively.

t+s=80, s=80-t

(0.2t+0.6s)/80=0.52  multiply both sides by 80

0.2t+0.6s=41.6, now using s=80-t in this equation gives us:

0.2t+0.6(80-t)=41.6  perform indicated multiplication on left side

0.2t+48-0.6t=41.6  combine like terms on left side

-0.4t+48=41.6  subtract 48 from both sides

-0.4t=-6.4  divide both sides by -0.4

t=16, since s=80-t

s=64

So 16kg of 20% alloy is mixed with 64kg of 60% allow to make 80kg of a 52% alloy.