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

Answer:

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

Step-by-step 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 $50 \times 0.60+x \times 0.25=\frac{1}{2}(50+x)$, as half of the final alloy has to be silver. Then solving for x

$30+0.25x=25+0.5x\\30-25=0.5x-0.25x\\5=0.25x\\x=\frac{5}{0.25}=20$

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.