Question

How many grams of an alloy containing 25% silver should be melted with 50 grams of an alloy containing 60% silver in order to obtain an alloy containing 50% silver?

Answer 1

20 grams of an alloy containing 25% silver has to be melted with 50 grams of an alloy containing 60% silver to obtain a final alloy containing 50% silver

Explanation:

Hi

We define

`A_(a)=50g @ 60\%`, wich means alloy a has 50 grams containing 60% silver.

`A_(b)=xg @ 25\%`, wich means alloy b has x grams containing 25% silver.

So we can build an equiation
`50 * 0.60+x * 0.25=(1)/(2)(50+x)`, as half of the final alloy has to be silver. Then solving for x

`30+0.25x=25+0.5x\\30-25=0.5x-0.25x\\5=0.25x\\x=(5)/(0.25)=20`

Wich means 20 grams of an alloy containing 25% silver (
`A_(b)`) has to be melted with 50 grams of an alloy containing 60% silver (
`A_(a)`) to obtain a final alloy containing 50% silver.