Question

Please help and explain!!!!!

Answer 1

Let $x$ be the amount of the 30% alloy and $y$ the amount of the 60% alloy the metalworker will use. However much is used, the final alloy will have a mass of

$x+y=100$

kilograms. For each kg of the 30% alloy used, 0.3 kg is copper; similary, each kg of the 60% alloy contributes 0.6 kg, so that

$0.3x+0.6y=0.54(x+y)=54$

Now,

$x+y=100\implies y=100-x$

$\implies0.3x+0.6(100-x)=54$

$\implies60-0.3x=54$

$\implies0.3x=6$

$\implies x=20$

$\implies y=100-20=80$