In two alloys, the ratios of copper to zinc are 5:2 and 3:4 (by weight). How many kg of the first alloy and of the second alloy should be alloyed together to obtain 28 kg of a new alloy with equal contents of copper and zinc?
Let x be the amount of first alloy mixed
let y be the amount of second alloy mixed
Copper in 1st alloy =57x
Total copper =5x+3y7
Zinc in 1st alloy =27x
Total Zinc =2x+4y7
Both copper & zinc should be in |:| ratio 5x+3y72x+4y7=1
5x+3y=2x+4y
3x=y ⟶(I)
we know both alloy should make 28kg
x+y=28 ⟶(II)
where y=3x
x+3x=28
x=7kg ⟶1st alloy
y=21kg ⟶2nd alloy