Question

Please help and explain!!!!!

A metalworker has a metal alloy that is 30​% copper and another alloy that is 60​% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 54​% copper​ alloy?

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`