Expert: Scott A Wilson - 10/22/2009

Question
An alloy containing 30% gold is mixed with a 60% gold alloy to get 300 kilograms of an alloy that is 50% gold. How many kilograms were used?

Answer
If N kilograms of alloy 1 were used, then 300-N kilograms of ally 2 were used.

Using this, there are 0.30N + 0.60(300-N) percent gold.

We wnat to find N the makes 0.30N + 0.60(300-N) = 0.50(300)

Multiplying out the parenthesis gives 0.3N + 180 - 0.6N = 150.

Combining the N's gives -0.3N + 180 = 150.

Adding 0.3N - 150 to both sides of the equation gives 30 = 0.3N.

This means N = 100.

So if we take 100 kilos of 30% gold and 200 kilos of 60% gold, we get 30 + 120 = 150.
And 150 is 50% of 300.